Solve for x x^4=2-|x|

$x^{4} = 2 - | x |$

Rewrite the equation as $2 - | x | = x^{4}$ .

$2 - | x | = x^{4}$

Subtract $2$ from both sides of the equation.

$- | x | = x^{4} - 2$

Divide each term in $- | x | = x^{4} - 2$ by $- 1$ and simplify.

Divide each term in $- | x | = x^{4} - 2$ by $- 1$ .

$\frac{- | x |}{- 1} = \frac{x^{4}}{- 1} + \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{| x |}{1} = \frac{x^{4}}{- 1} + \frac{- 2}{- 1}$

Divide $| x |$ by $1$ .

$| x | = \frac{x^{4}}{- 1} + \frac{- 2}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{x^{4}}{- 1}$ .

$| x | = - 1 \cdot x^{4} + \frac{- 2}{- 1}$

Rewrite $- 1 \cdot x^{4}$ as $- x^{4}$ .

$| x | = - x^{4} + \frac{- 2}{- 1}$

Divide $- 2$ by $- 1$ .

$| x | = - x^{4} + 2$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x = \pm (- x^{4} + 2)$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = - x^{4} + 2$

Reorder the polynomial.

$x^{4} + x - 2$

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

$p = \pm 1, \pm 2$

$q = \pm 1$

Find every combination of $\pm \frac{p}{q}$ . These are the possible roots of the polynomial function.

$\pm 1, \pm 2$

Substitute the possible roots one by one into the polynomial to find the actual roots. Simplify to check if the value is $0$ , which means it is a root.

$(1) + {(1)}^{4} - 2$

Simplify the expression. In this case, the expression is equal to $0$ so $x = 1$ is a root of the polynomial.

One to any power is one.

$1 + 1 - 2$

Add $1$ and $1$ .

$2 - 2$

Subtract $2$ from $2$ .

$0$

Since $1$ is a known root, divide the polynomial by $x - 1$ to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

$\frac{x + x^{4} - 2}{x - 1}$

Next, find the roots of the remaining polynomial. The order of the polynomial has been reduced by $1$ .

Place the numbers representing the divisor and the dividend into a division-like configuration.

$1$	$1$	$0$	$0$	$1$	$- 2$
	\xa0				\xa0

The first number in the dividend $(1)$ is put into the first position of the result area (below the horizontal line).

$1$	$1$	$0$	$0$	$1$	$- 2$
	\xa0				\xa0
	$1$

Multiply the newest entry in the result $(1)$ by the divisor $(1)$ and place the result of $(1)$ under the next term in the dividend $(0)$ .

$1$	$1$	$0$	$0$	$1$	$- 2$
	\xa0	$1$			\xa0
	$1$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$1$	$1$	$0$	$0$	$1$	$- 2$
	\xa0	$1$			\xa0
	$1$	$1$

Multiply the newest entry in the result $(1)$ by the divisor $(1)$ and place the result of $(1)$ under the next term in the dividend $(0)$ .

$1$	$1$	$0$	$0$	$1$	$- 2$
	\xa0	$1$	$1$		\xa0
	$1$	$1$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$1$	$1$	$0$	$0$	$1$	$- 2$
	\xa0	$1$	$1$		\xa0
	$1$	$1$	$1$

Multiply the newest entry in the result $(1)$ by the divisor $(1)$ and place the result of $(1)$ under the next term in the dividend $(1)$ .

$1$	$1$	$0$	$0$	$1$	$- 2$
	\xa0	$1$	$1$	$1$	\xa0
	$1$	$1$	$1$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$1$	$1$	$0$	$0$	$1$	$- 2$
	\xa0	$1$	$1$	$1$	\xa0
	$1$	$1$	$1$	$2$

Multiply the newest entry in the result $(2)$ by the divisor $(1)$ and place the result of $(2)$ under the next term in the dividend $(- 2)$ .

$1$	$1$	$0$	$0$	$1$	$- 2$
	\xa0	$1$	$1$	$1$	$2$
	$1$	$1$	$1$	$2$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$1$	$1$	$0$	$0$	$1$	$- 2$
	\xa0	$1$	$1$	$1$	$2$
	$1$	$1$	$1$	$2$	$0$

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

$1 x^{3} + 1 x^{2} + (1) x + 2$

Simplify the quotient polynomial.

$x^{3} + x^{2} + x + 2$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 1.35320996$

The polynomial can be written as a set of linear factors.

$(x - 1) (x + 1.35320996)$

These are the roots (zeros) of the polynomial $x^{4} + x - 2$ .

$x = 1, - 1.35320996$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - (- x^{4} + 2)$

Simplify $- (- x^{4} + 2)$ .

Apply the distributive property.

$x = - - x^{4} - 1 \cdot 2$

Multiply $- - x^{4}$ .

Multiply $- 1$ by $- 1$ .

$x = 1 x^{4} - 1 \cdot 2$

Multiply $x^{4}$ by $1$ .

$x = x^{4} - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$x = x^{4} - 2$

Subtract $x^{4}$ from both sides of the equation.

$x - x^{4} = - 2$

Add $2$ to both sides of the equation.

$x - x^{4} + 2 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $x - x^{4} + 2$ .

Reorder $x$ and $- x^{4}$ .

$- x^{4} + x + 2 = 0$

Factor $- 1$ out of $- x^{4}$ .

$- (x^{4}) + x + 2 = 0$

Factor $- 1$ out of $x$ .

$- (x^{4}) - 1 (- x) + 2 = 0$

Rewrite $2$ as $- 1 (- 2)$ .

$- (x^{4}) - 1 (- x) - 1 \cdot - 2 = 0$

Factor $- 1$ out of $- (x^{4}) - 1 (- x)$ .

$- (x^{4} - x) - 1 \cdot - 2 = 0$

Factor $- 1$ out of $- (x^{4} - x) - 1 (- 2)$ .

$- (x^{4} - x - 2) = 0$

Factor.

Factor $x^{4} - x - 2$ using the rational roots test.

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

$p = \pm 1, \pm 2 q = \pm 1$

Find every combination of $\pm \frac{p}{q}$ . These are the possible roots of the polynomial function.

$\pm 1, \pm 2$

Substitute $- 1$ and simplify the expression. In this case, the expression is equal to $0$ so $- 1$ is a root of the polynomial.

Substitute $- 1$ into the polynomial.

${(- 1)}^{4} - - 1 - 2$

Raise $- 1$ to the power of $4$ .

$1 - - 1 - 2$

Multiply $- 1$ by $- 1$ .

$1 + 1 - 2$

Add $1$ and $1$ .

$2 - 2$

Subtract $2$ from $2$ .

$0$

Since $- 1$ is a known root, divide the polynomial by $x + 1$ to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

$\frac{x^{4} - x - 2}{x + 1}$

Divide $x^{4} - x - 2$ by $x + 1$ .

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

Divide the highest order term in the dividend $x^{4}$ by the highest order term in divisor $x$ .

$x^{3}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

Multiply the new quotient term by the divisor.

$x^{3}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

The expression needs to be subtracted from the dividend, so change all the signs in $x^{4} + x^{3}$

$x^{3}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

Pull the next terms from the original dividend down into the current dividend.

$x^{3}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

Divide the highest order term in the dividend $- x^{3}$ by the highest order term in divisor $x$ .

$x^{3}$

$x^{2}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

Multiply the new quotient term by the divisor.

$x^{3}$

$x^{2}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

The expression needs to be subtracted from the dividend, so change all the signs in $- x^{3} - x^{2}$

$x^{3}$

$x^{2}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$x^{2}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

Pull the next terms from the original dividend down into the current dividend.

$x^{3}$

$x^{2}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

$x$

Divide the highest order term in the dividend $x^{2}$ by the highest order term in divisor $x$ .

$x^{3}$

$x^{2}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

$x$

Multiply the new quotient term by the divisor.

$x^{3}$

$x^{2}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

$x$

$x^{2}$

$x$

The expression needs to be subtracted from the dividend, so change all the signs in $x^{2} + x$

$x^{3}$

$x^{2}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

$x$

$x^{2}$

$x$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$x^{2}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

$x$

$x^{2}$

$x$

$2 x$

Pull the next terms from the original dividend down into the current dividend.

$x^{3}$

$x^{2}$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

$x$

$x^{2}$

$x$

$2 x$

$2$

Divide the highest order term in the dividend $- 2 x$ by the highest order term in divisor $x$ .

$x^{3}$

$x^{2}$

$x$

$2$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

$x$

$x^{2}$

$x$

$2 x$

$2$

Multiply the new quotient term by the divisor.

				$x^{3}$	-	$x^{2}$	+	$x$	-	$2$
$x$	+	$1$		$x^{4}$	+	$0 x^{3}$	+	$0 x^{2}$	-	$x$	-	$2$
			-	$x^{4}$	-	$x^{3}$
					-	$x^{3}$	+	$0 x^{2}$
					+	$x^{3}$	+	$x^{2}$
							+	$x^{2}$	-	$x$
							-	$x^{2}$	-	$x$
									-	$2 x$	-	$2$
									-	$2 x$	-	$2$

The expression needs to be subtracted from the dividend, so change all the signs in $- 2 x - 2$

$x^{3}$

$x^{2}$

$x$

$2$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

$x$

$x^{2}$

$x$

$2 x$

$2$

$2 x$

$2$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$x^{2}$

$x$

$2$

$x$

$1$

$x^{4}$

$0 x^{3}$

$0 x^{2}$

$x$

$2$

$x^{4}$

$x^{3}$

$0 x^{2}$

$x^{3}$

$x^{2}$

$x$

$x^{2}$

$x$

$2 x$

$2$

$2 x$

$2$

$0$

Since the remander is $0$ , the final answer is the quotient.

$x^{3} - x^{2} + x - 2$

Write $x^{4} - x - 2$ as a set of factors.

$- ((x + 1) (x^{3} - x^{2} + x - 2)) = 0$

Remove unnecessary parentheses.

$- (x + 1) (x^{3} - x^{2} + x - 2) = 0$

Divide each term in $- (x + 1) (x^{3} - x^{2} + x - 2) = 0$ by $- 1$ and simplify.

Divide each term in $- (x + 1) (x^{3} - x^{2} + x - 2) = 0$ by $- 1$ .

$\frac{- (x + 1) (x^{3} - x^{2} + x - 2)}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Reduce the expression by cancelling the common factors.

Dividing two negative values results in a positive value.

$\frac{(x + 1) (x^{3} - x^{2} + x - 2)}{1} = \frac{0}{- 1}$

Divide $(x + 1) (x^{3} - x^{2} + x - 2)$ by $1$ .

$(x + 1) (x^{3} - x^{2} + x - 2) = \frac{0}{- 1}$

Expand $(x + 1) (x^{3} - x^{2} + x - 2)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x^{3} + x (- x^{2}) + x \cdot x + x \cdot - 2 + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Simplify terms.

Simplify each term.

Multiply $x$ by $x^{3}$ by adding the exponents.

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$x^{1} x^{3} + x (- x^{2}) + x \cdot x + x \cdot - 2 + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{1 + 3} + x (- x^{2}) + x \cdot x + x \cdot - 2 + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Add $1$ and $3$ .

$x^{4} + x (- x^{2}) + x \cdot x + x \cdot - 2 + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Rewrite using the commutative property of multiplication.

$x^{4} - x \cdot x^{2} + x \cdot x + x \cdot - 2 + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$x^{4} - (x^{2} x) + x \cdot x + x \cdot - 2 + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$x^{4} - (x^{2} x^{1}) + x \cdot x + x \cdot - 2 + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{4} - x^{2 + 1} + x \cdot x + x \cdot - 2 + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Add $2$ and $1$ .

$x^{4} - x^{3} + x \cdot x + x \cdot - 2 + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Multiply $x$ by $x$ .

$x^{4} - x^{3} + x^{2} + x \cdot - 2 + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Move $- 2$ to the left of $x$ .

$x^{4} - x^{3} + x^{2} - 2 \cdot x + 1 x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Multiply $x^{3}$ by $1$ .

$x^{4} - x^{3} + x^{2} - 2 x + x^{3} + 1 (- x^{2}) + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Multiply $- x^{2}$ by $1$ .

$x^{4} - x^{3} + x^{2} - 2 x + x^{3} - x^{2} + 1 x + 1 \cdot - 2 = \frac{0}{- 1}$

Multiply $x$ by $1$ .

$x^{4} - x^{3} + x^{2} - 2 x + x^{3} - x^{2} + x + 1 \cdot - 2 = \frac{0}{- 1}$

Multiply $- 2$ by $1$ .

$x^{4} - x^{3} + x^{2} - 2 x + x^{3} - x^{2} + x - 2 = \frac{0}{- 1}$

Simplify by adding terms.

Combine the opposite terms in $x^{4} - x^{3} + x^{2} - 2 x + x^{3} - x^{2} + x - 2$ .

Add $- x^{3}$ and $x^{3}$ .

$x^{4} + x^{2} - 2 x + 0 - x^{2} + x - 2 = \frac{0}{- 1}$

Add $x^{4} + x^{2} - 2 x$ and $0$ .

$x^{4} + x^{2} - 2 x - x^{2} + x - 2 = \frac{0}{- 1}$

Subtract $x^{2}$ from $x^{2}$ .

$x^{4} - 2 x + 0 + x - 2 = \frac{0}{- 1}$

Add $x^{4} - 2 x$ and $0$ .

$x^{4} - 2 x + x - 2 = \frac{0}{- 1}$

Add $- 2 x$ and $x$ .

$x^{4} - x - 2 = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

$x^{4} - x - 2 = 0$

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

$p = \pm 1, \pm 2$

$q = \pm 1$

Find every combination of $\pm \frac{p}{q}$ . These are the possible roots of the polynomial function.

$\pm 1, \pm 2$

Substitute the possible roots one by one into the polynomial to find the actual roots. Simplify to check if the value is $0$ , which means it is a root.

${(- 1)}^{4} - (- 1) - 2$

Simplify the expression. In this case, the expression is equal to $0$ so $x = - 1$ is a root of the polynomial.

Simplify each term.

Raise $- 1$ to the power of $4$ .

$1 - (- 1) - 2$

Multiply $- 1$ by $- 1$ .

$1 + 1 - 2$

Simplify by adding and subtracting.

Add $1$ and $1$ .

$2 - 2$

Subtract $2$ from $2$ .

$0$

Since $- 1$ is a known root, divide the polynomial by $x + 1$ to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

$\frac{x^{4} - x - 2}{x + 1}$

Next, find the roots of the remaining polynomial. The order of the polynomial has been reduced by $1$ .

Place the numbers representing the divisor and the dividend into a division-like configuration.

$- 1$	$1$	$0$	$0$	$- 1$	$- 2$
	\xa0				\xa0

The first number in the dividend $(1)$ is put into the first position of the result area (below the horizontal line).

$- 1$	$1$	$0$	$0$	$- 1$	$- 2$
	\xa0				\xa0
	$1$

Multiply the newest entry in the result $(1)$ by the divisor $(- 1)$ and place the result of $(- 1)$ under the next term in the dividend $(0)$ .

$- 1$	$1$	$0$	$0$	$- 1$	$- 2$
	\xa0	$- 1$			\xa0
	$1$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$- 1$	$1$	$0$	$0$	$- 1$	$- 2$
	\xa0	$- 1$			\xa0
	$1$	$- 1$

Multiply the newest entry in the result $(- 1)$ by the divisor $(- 1)$ and place the result of $(1)$ under the next term in the dividend $(0)$ .

$- 1$	$1$	$0$	$0$	$- 1$	$- 2$
	\xa0	$- 1$	$1$		\xa0
	$1$	$- 1$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$- 1$	$1$	$0$	$0$	$- 1$	$- 2$
	\xa0	$- 1$	$1$		\xa0
	$1$	$- 1$	$1$

Multiply the newest entry in the result $(1)$ by the divisor $(- 1)$ and place the result of $(- 1)$ under the next term in the dividend $(- 1)$ .

$- 1$	$1$	$0$	$0$	$- 1$	$- 2$
	\xa0	$- 1$	$1$	$- 1$	\xa0
	$1$	$- 1$	$1$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$- 1$	$1$	$0$	$0$	$- 1$	$- 2$
	\xa0	$- 1$	$1$	$- 1$	\xa0
	$1$	$- 1$	$1$	$- 2$

Multiply the newest entry in the result $(- 2)$ by the divisor $(- 1)$ and place the result of $(2)$ under the next term in the dividend $(- 2)$ .

$- 1$	$1$	$0$	$0$	$- 1$	$- 2$
	\xa0	$- 1$	$1$	$- 1$	$2$
	$1$	$- 1$	$1$	$- 2$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$- 1$	$1$	$0$	$0$	$- 1$	$- 2$
	\xa0	$- 1$	$1$	$- 1$	$2$
	$1$	$- 1$	$1$	$- 2$	$0$

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

$1 x^{3} + - 1 x^{2} + (1) x - 2$

Simplify the quotient polynomial.

$x^{3} - x^{2} + x - 2$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 1.35320996$

The polynomial can be written as a set of linear factors.

$(x + 1) (x - 1.35320996)$

These are the roots (zeros) of the polynomial $x^{4} - x - 2$ .

$x = - 1, 1.35320996$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 1.35320996, - 1, 1.35320996$

Exclude the solutions that do not make $x^{4} = 2 - | x |$ true.

$x = 1, - 1$

Solve for x x^4=2-|x|

Related Questions

Support LCMGCF.com by disabling your adblocker.