Solve for x 10=2 square root of x-8

$10 = 2 \sqrt{x - 8}$

Step 1

Rewrite the equation as $2 \sqrt{x - 8} = 10$ .

$2 \sqrt{x - 8} = 10$

Step 2

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

${(2 \sqrt{x - 8})}^{2} = 10^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 8}$ as ${(x - 8)}^{\frac{1}{2}}$ .

${(2 {(x - 8)}^{\frac{1}{2}})}^{2} = 10^{2}$

Simplify the left side.

Simplify ${(2 {(x - 8)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $2 {(x - 8)}^{\frac{1}{2}}$ .

$2^{2} {({(x - 8)}^{\frac{1}{2}})}^{2} = 10^{2}$

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

$4 {({(x - 8)}^{\frac{1}{2}})}^{2} = 10^{2}$

Multiply the exponents in ${({(x - 8)}^{\frac{1}{2}})}^{2}$ .

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

$4 {(x - 8)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(x - 8)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Rewrite the expression.

$4 {(x - 8)}^{1} = 10^{2}$

Simplify.

$4 (x - 8) = 10^{2}$

Apply the distributive property.

$4 x + 4 \cdot - 8 = 10^{2}$

Multiply $4$ by $- 8$ .

$4 x - 32 = 10^{2}$

Simplify the right side.

Raise $10$ to the power of $2$ .

$4 x - 32 = 100$

Step 4

Solve for $x$ .

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

Add $32$ to both sides of the equation.

$4 x = 100 + 32$

Add $100$ and $32$ .

$4 x = 132$

Divide each term in $4 x = 132$ by $4$ and simplify.

Divide each term in $4 x = 132$ by $4$ .

$\frac{4 x}{4} = \frac{132}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{132}{4}$

Divide $x$ by $1$ .

$x = \frac{132}{4}$

Simplify the right side.

Divide $132$ by $4$ .

$x = 33$

Solve for x 10=2 square root of x-8

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