Evaluate square root of 2x+2 = square root of x+10

$\sqrt{2 x + 2} = \sqrt{x + 10}$

Step 1

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

${\sqrt{2 x + 2}}^{2} = {\sqrt{x + 10}}^{2}$

Step 2

Simplify each side of the equation.

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

${({(2 x + 2)}^{\frac{1}{2}})}^{2} = {\sqrt{x + 10}}^{2}$

Simplify the left side.

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

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

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

${(2 x + 2)}^{\frac{1}{2} \cdot 2} = {\sqrt{x + 10}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x + 2)}^{\frac{1}{2} \cdot 2} = {\sqrt{x + 10}}^{2}$

Rewrite the expression.

${(2 x + 2)}^{1} = {\sqrt{x + 10}}^{2}$

Simplify.

$2 x + 2 = {\sqrt{x + 10}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{x + 10}}^{2}$ as $x + 10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 10}$ as ${(x + 10)}^{\frac{1}{2}}$ .

$2 x + 2 = {({(x + 10)}^{\frac{1}{2}})}^{2}$

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

$2 x + 2 = {(x + 10)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$2 x + 2 = {(x + 10)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 x + 2 = {(x + 10)}^{\frac{2}{2}}$

Rewrite the expression.

$2 x + 2 = {(x + 10)}^{1}$

Simplify.

$2 x + 2 = x + 10$

Step 3

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$2 x + 2 - x = 10$

Subtract $x$ from $2 x$ .

$x + 2 = 10$

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$x = 10 - 2$

Subtract $2$ from $10$ .

$x = 8$

Evaluate square root of 2x+2 = square root of x+10

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