Solve by Factoring square root of x+2-15=-3

$\sqrt{x + 2} - 15 = - 3$

Step 1

Add $3$ to both sides of the equation.

$\sqrt{x + 2} - 15 + 3 = 0$

Step 2

Add $- 15$ and $3$ .

$\sqrt{x + 2} - 12 = 0$

Step 3

Add $12$ to both sides of the equation.

$\sqrt{x + 2} = 12$

Step 4

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

${\sqrt{x + 2}}^{2} = 12^{2}$

Step 5

Simplify each side of the equation.

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

${({(x + 2)}^{\frac{1}{2}})}^{2} = 12^{2}$

Simplify the left side.

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

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

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

${(x + 2)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 2)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Rewrite the expression.

${(x + 2)}^{1} = 12^{2}$

Simplify.

$x + 2 = 12^{2}$

Simplify the right side.

Raise $12$ to the power of $2$ .

$x + 2 = 144$

Step 6

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

Subtract $2$ from both sides of the equation.

$x = 144 - 2$

Subtract $2$ from $144$ .

$x = 142$