Solve by Factoring x- square root of 1-x=-5

$x - \sqrt{1 - x} = - 5$

Step 1

Add $5$ to both sides of the equation.

$x - \sqrt{1 - x} + 5 = 0$

Step 2

Move all terms not containing $- \sqrt{1 - x}$ to the right side of the equation.

Subtract $x$ from both sides of the equation.

$- \sqrt{1 - x} + 5 = - x$

Subtract $5$ from both sides of the equation.

$- \sqrt{1 - x} = - x - 5$

Step 3

To remove the radical on the left side of the equation, square both sides of the equation.

${(- \sqrt{1 - x})}^{2} = {(- x - 5)}^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{1 - x}$ as ${(1 - x)}^{\frac{1}{2}}$ .

${(- {(1 - x)}^{\frac{1}{2}})}^{2} = {(- x - 5)}^{2}$

Simplify the left side.

Simplify ${(- {(1 - x)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- {(1 - x)}^{\frac{1}{2}}$ .

${(- 1)}^{2} {({(1 - x)}^{\frac{1}{2}})}^{2} = {(- x - 5)}^{2}$

Raise $- 1$ to the power of $2$ .

$1 {({(1 - x)}^{\frac{1}{2}})}^{2} = {(- x - 5)}^{2}$

Multiply ${({(1 - x)}^{\frac{1}{2}})}^{2}$ by $1$ .

${({(1 - x)}^{\frac{1}{2}})}^{2} = {(- x - 5)}^{2}$

Multiply the exponents in ${({(1 - x)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(1 - x)}^{\frac{1}{2} \cdot 2} = {(- x - 5)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(1 - x)}^{\frac{1}{2} \cdot 2} = {(- x - 5)}^{2}$

Rewrite the expression.

${(1 - x)}^{1} = {(- x - 5)}^{2}$

Simplify.

$1 - x = {(- x - 5)}^{2}$

Simplify the right side.

Simplify ${(- x - 5)}^{2}$ .

Rewrite ${(- x - 5)}^{2}$ as $(- x - 5) (- x - 5)$ .

$1 - x = (- x - 5) (- x - 5)$

Expand $(- x - 5) (- x - 5)$ using the FOIL Method.

Apply the distributive property.

$1 - x = - x (- x - 5) - 5 (- x - 5)$

Apply the distributive property.

$1 - x = - x (- x) - x \cdot - 5 - 5 (- x - 5)$

Apply the distributive property.

$1 - x = - x (- x) - x \cdot - 5 - 5 (- x) - 5 \cdot - 5$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$1 - x = - 1 \cdot - 1 x \cdot x - x \cdot - 5 - 5 (- x) - 5 \cdot - 5$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$1 - x = - 1 \cdot - 1 (x \cdot x) - x \cdot - 5 - 5 (- x) - 5 \cdot - 5$

Multiply $x$ by $x$ .

$1 - x = - 1 \cdot - 1 x^{2} - x \cdot - 5 - 5 (- x) - 5 \cdot - 5$

Multiply $- 1$ by $- 1$ .

$1 - x = 1 x^{2} - x \cdot - 5 - 5 (- x) - 5 \cdot - 5$

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

$1 - x = x^{2} - x \cdot - 5 - 5 (- x) - 5 \cdot - 5$

Multiply $- 5$ by $- 1$ .

$1 - x = x^{2} + 5 x - 5 (- x) - 5 \cdot - 5$

Multiply $- 1$ by $- 5$ .

$1 - x = x^{2} + 5 x + 5 x - 5 \cdot - 5$

Multiply $- 5$ by $- 5$ .

$1 - x = x^{2} + 5 x + 5 x + 25$

Add $5 x$ and $5 x$ .

$1 - x = x^{2} + 10 x + 25$

Step 5

Solve for $x$ .

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} + 10 x + 25 = 1 - x$

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$x^{2} + 10 x + 25 + x = 1$

Add $10 x$ and $x$ .

$x^{2} + 11 x + 25 = 1$

Subtract $1$ from both sides of the equation.

$x^{2} + 11 x + 25 - 1 = 0$

Subtract $1$ from $25$ .

$x^{2} + 11 x + 24 = 0$

Factor $x^{2} + 11 x + 24$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $24$ and whose sum is $11$ .

$3, 8$

Write the factored form using these integers.

$(x + 3) (x + 8) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 3 = 0$

$x + 8 = 0$

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Set $x + 8$ equal to $0$ and solve for $x$ .

Set $x + 8$ equal to $0$ .

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$

The final solution is all the values that make $(x + 3) (x + 8) = 0$ true.

$x = - 3, - 8$

Step 6

Exclude the solutions that do not make $x - \sqrt{1 - x} + 5 = 0$ true.

$x = - 3$

Solve by Factoring x- square root of 1-x=-5

Related Questions

Support LCMGCF.com by disabling your adblocker.