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

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

Step 1

Add $10$ to both sides of the equation.

$5 \sqrt{x + 7} + 10 = 0$

Step 2

Factor $5$ out of $5 \sqrt{x + 7} + 10$ .

Factor $5$ out of $5 \sqrt{x + 7}$ .

$5 (\sqrt{x + 7}) + 10 = 0$

Factor $5$ out of $10$ .

$5 \sqrt{x + 7} + 5 \cdot 2 = 0$

Factor $5$ out of $5 \sqrt{x + 7} + 5 \cdot 2$ .

$5 (\sqrt{x + 7} + 2) = 0$

Step 3

Divide each term in $5 (\sqrt{x + 7} + 2) = 0$ by $5$ and simplify.

Divide each term in $5 (\sqrt{x + 7} + 2) = 0$ by $5$ .

$\frac{5 (\sqrt{x + 7} + 2)}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (\sqrt{x + 7} + 2)}{5} = \frac{0}{5}$

Divide $\sqrt{x + 7} + 2$ by $1$ .

$\sqrt{x + 7} + 2 = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$\sqrt{x + 7} + 2 = 0$

Step 4

Subtract $2$ from both sides of the equation.

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

Step 5

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

${\sqrt{x + 7}}^{2} = {(- 2)}^{2}$

Step 6

Simplify each side of the equation.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x + 7 = {(- 2)}^{2}$

Simplify the right side.

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

$x + 7 = 4$

Step 7

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

Subtract $7$ from both sides of the equation.

$x = 4 - 7$

Subtract $7$ from $4$ .

$x = - 3$

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

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