Solve by Factoring 3 square root of x+5=-9

$3 \sqrt{x + 5} = - 9$

Step 1

Add $9$ to both sides of the equation.

$3 \sqrt{x + 5} + 9 = 0$

Step 2

Factor $3$ out of $3 \sqrt{x + 5} + 9$ .

Factor $3$ out of $3 \sqrt{x + 5}$ .

$3 (\sqrt{x + 5}) + 9 = 0$

Factor $3$ out of $9$ .

$3 \sqrt{x + 5} + 3 \cdot 3 = 0$

Factor $3$ out of $3 \sqrt{x + 5} + 3 \cdot 3$ .

$3 (\sqrt{x + 5} + 3) = 0$

Step 3

Divide each term in $3 (\sqrt{x + 5} + 3) = 0$ by $3$ and simplify.

Divide each term in $3 (\sqrt{x + 5} + 3) = 0$ by $3$ .

$\frac{3 (\sqrt{x + 5} + 3)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (\sqrt{x + 5} + 3)}{3} = \frac{0}{3}$

Divide $\sqrt{x + 5} + 3$ by $1$ .

$\sqrt{x + 5} + 3 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$\sqrt{x + 5} + 3 = 0$

Step 4

Subtract $3$ from both sides of the equation.

$\sqrt{x + 5} = - 3$

Step 5

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

${\sqrt{x + 5}}^{2} = {(- 3)}^{2}$

Step 6

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 5}$ as ${(x + 5)}^{\frac{1}{2}}$ .

${({(x + 5)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

Simplify the left side.

Simplify ${({(x + 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x + 5)}^{\frac{1}{2}})}^{2}$ .

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

${(x + 5)}^{\frac{1}{2} \cdot 2} = {(- 3)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 5)}^{\frac{1}{2} \cdot 2} = {(- 3)}^{2}$

Rewrite the expression.

${(x + 5)}^{1} = {(- 3)}^{2}$

Simplify.

$x + 5 = {(- 3)}^{2}$

Simplify the right side.

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

$x + 5 = 9$

Step 7

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

Subtract $5$ from both sides of the equation.

$x = 9 - 5$

Subtract $5$ from $9$ .

$x = 4$

Step 8

Exclude the solutions that do not make $3 (\sqrt{x + 5} + 3) = 0$ true.

$No solution$

Solve by Factoring 3 square root of x+5=-9

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