Solve for x 4 square root of x+1=x+1

$4 \sqrt{x + 1} = x + 1$

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

${(4 \sqrt{x + 1})}^{2} = {(x + 1)}^{2}$

Simplify each side of the equation.

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

${(4 {(x + 1)}^{\frac{1}{2}})}^{2} = {(x + 1)}^{2}$

Simplify the left side.

Simplify ${(4 {(x + 1)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $4 {(x + 1)}^{\frac{1}{2}}$ .

$4^{2} {({(x + 1)}^{\frac{1}{2}})}^{2} = {(x + 1)}^{2}$

Raise $4$ to the power of $2$ .

$16 {({(x + 1)}^{\frac{1}{2}})}^{2} = {(x + 1)}^{2}$

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

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

$16 {(x + 1)}^{\frac{1}{2} \cdot 2} = {(x + 1)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 {(x + 1)}^{\frac{1}{2} \cdot 2} = {(x + 1)}^{2}$

Rewrite the expression.

$16 {(x + 1)}^{1} = {(x + 1)}^{2}$

Simplify.

$16 (x + 1) = {(x + 1)}^{2}$

Apply the distributive property.

$16 x + 16 \cdot 1 = {(x + 1)}^{2}$

Multiply $16$ by $1$ .

$16 x + 16 = {(x + 1)}^{2}$

Simplify the right side.

Simplify ${(x + 1)}^{2}$ .

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$16 x + 16 = (x + 1) (x + 1)$

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$16 x + 16 = x (x + 1) + 1 (x + 1)$

Apply the distributive property.

$16 x + 16 = x \cdot x + x \cdot 1 + 1 (x + 1)$

Apply the distributive property.

$16 x + 16 = x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$16 x + 16 = x^{2} + x \cdot 1 + 1 x + 1 \cdot 1$

Multiply $x$ by $1$ .

$16 x + 16 = x^{2} + x + 1 x + 1 \cdot 1$

Multiply $x$ by $1$ .

$16 x + 16 = x^{2} + x + x + 1 \cdot 1$

Multiply $1$ by $1$ .

$16 x + 16 = x^{2} + x + x + 1$

Add $x$ and $x$ .

$16 x + 16 = x^{2} + 2 x + 1$

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.

$x^{2} + 2 x + 1 = 16 x + 16$

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

Subtract $16 x$ from both sides of the equation.

$x^{2} + 2 x + 1 - 16 x = 16$

Subtract $16 x$ from $2 x$ .

$x^{2} - 14 x + 1 = 16$

Subtract $16$ from both sides of the equation.

$x^{2} - 14 x + 1 - 16 = 0$

Subtract $16$ from $1$ .

$x^{2} - 14 x - 15 = 0$

Factor $x^{2} - 14 x - 15$ 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 $- 15$ and whose sum is $- 14$ .

$- 15, 1$

Write the factored form using these integers.

$(x - 15) (x + 1) = 0$

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

$x - 15 = 0$

$x + 1 = 0$

Set $x - 15$ equal to $0$ and solve for $x$ .

Set $x - 15$ equal to $0$ .

$x - 15 = 0$

Add $15$ to both sides of the equation.

$x = 15$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make $(x - 15) (x + 1) = 0$ true.

$x = 15, - 1$

Solve for x 4 square root of x+1=x+1

Related Questions

Support LCMGCF.com by disabling your adblocker.