Solve for x -2=-5+ square root of x+7

$- 2 = - 5 + \sqrt{x + 7}$

Rewrite the equation as $- 5 + \sqrt{x + 7} = - 2$ .

$- 5 + \sqrt{x + 7} = - 2$

Move all terms not containing $\sqrt{x + 7}$ to the right side of the equation.

Add $5$ to both sides of the equation.

$\sqrt{x + 7} = - 2 + 5$

Add $- 2$ and $5$ .

$\sqrt{x + 7} = 3$

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

${\sqrt{x + 7}}^{2} = 3^{2}$

Simplify each side of the equation.

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

${({(x + 7)}^{\frac{1}{2}})}^{2} = 3^{2}$

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, ${(a^{m})}^{n} = a^{m n}$ .

${(x + 7)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 7)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(x + 7)}^{1} = 3^{2}$

Simplify.

$x + 7 = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$x + 7 = 9$

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

Subtract $7$ from both sides of the equation.

$x = 9 - 7$

Subtract $7$ from $9$ .

$x = 2$