Find All Complex Solutions square root of x+10-7=-5

$\sqrt{x + 10} - 7 = - 5$

Step 1

Move all terms not containing $\sqrt{x + 10}$ to the right side of the equation.

Add $7$ to both sides of the equation.

$\sqrt{x + 10} = - 5 + 7$

Add $- 5$ and $7$ .

$\sqrt{x + 10} = 2$

Step 2

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

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

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

Multiply the exponents in ${({(x + 10)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x + 10 = 2^{2}$

Simplify the right side.

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

$x + 10 = 4$

Step 4

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

Subtract $10$ from both sides of the equation.

$x = 4 - 10$

Subtract $10$ from $4$ .

$x = - 6$