Solve by Factoring square root of x-7=15

$\sqrt{x - 7} = 15$

Step 1

Subtract $15$ from both sides of the equation.

$\sqrt{x - 7} - 15 = 0$

Step 2

Add $15$ to both sides of the equation.

$\sqrt{x - 7} = 15$

Step 3

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

${\sqrt{x - 7}}^{2} = 15^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 7}$ as ${(x - 7)}^{\frac{1}{2}}$ .

${({(x - 7)}^{\frac{1}{2}})}^{2} = 15^{2}$

Simplify the left side.

Simplify ${({(x - 7)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x - 7)}^{\frac{1}{2}})}^{2}$ .

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

${(x - 7)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x - 7)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Rewrite the expression.

${(x - 7)}^{1} = 15^{2}$

Simplify.

$x - 7 = 15^{2}$

Simplify the right side.

Raise $15$ to the power of $2$ .

$x - 7 = 225$

Step 5

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

Add $7$ to both sides of the equation.

$x = 225 + 7$

Add $225$ and $7$ .

$x = 232$