Solve for x 3 square root of x+5=-9

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

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

${(3 \sqrt{x + 5})}^{2} = {(- 9)}^{2}$

Simplify each side of the equation.

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

${(3 {(x + 5)}^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Simplify the left side.

Simplify ${(3 {(x + 5)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $3 {(x + 5)}^{\frac{1}{2}}$ .

$3^{2} {({(x + 5)}^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

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

$9 {({(x + 5)}^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

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

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

$9 {(x + 5)}^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 {(x + 5)}^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Rewrite the expression.

$9 {(x + 5)}^{1} = {(- 9)}^{2}$

Simplify.

$9 (x + 5) = {(- 9)}^{2}$

Apply the distributive property.

$9 x + 9 \cdot 5 = {(- 9)}^{2}$

Multiply $9$ by $5$ .

$9 x + 45 = {(- 9)}^{2}$

Simplify the right side.

Raise $- 9$ to the power of $2$ .

$9 x + 45 = 81$

Solve for $x$ .

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

Subtract $45$ from both sides of the equation.

$9 x = 81 - 45$

Subtract $45$ from $81$ .

$9 x = 36$

Divide each term in $9 x = 36$ by $9$ and simplify.

Divide each term in $9 x = 36$ by $9$ .

$\frac{9 x}{9} = \frac{36}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{36}{9}$

Divide $x$ by $1$ .

$x = \frac{36}{9}$

Simplify the right side.

Divide $36$ by $9$ .

$x = 4$

Exclude the solutions that do not make $3 \sqrt{x + 5} = - 9$ true.

$No solution$

Solve for x 3 square root of x+5=-9

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