Solve for x square root of x+11 = square root of -1-3x

$\sqrt{x + 11} = \sqrt{- 1 - 3 x}$

Step 1

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

${\sqrt{x + 11}}^{2} = {\sqrt{- 1 - 3 x}}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 11}$ as ${(x + 11)}^{\frac{1}{2}}$ .

${({(x + 11)}^{\frac{1}{2}})}^{2} = {\sqrt{- 1 - 3 x}}^{2}$

Simplify the left side.

Simplify ${({(x + 11)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x + 11)}^{\frac{1}{2}})}^{2}$ .

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

${(x + 11)}^{\frac{1}{2} \cdot 2} = {\sqrt{- 1 - 3 x}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 11)}^{\frac{1}{2} \cdot 2} = {\sqrt{- 1 - 3 x}}^{2}$

Rewrite the expression.

${(x + 11)}^{1} = {\sqrt{- 1 - 3 x}}^{2}$

Simplify.

$x + 11 = {\sqrt{- 1 - 3 x}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{- 1 - 3 x}}^{2}$ as $- 1 - 3 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{- 1 - 3 x}$ as ${(- 1 - 3 x)}^{\frac{1}{2}}$ .

$x + 11 = {({(- 1 - 3 x)}^{\frac{1}{2}})}^{2}$

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

$x + 11 = {(- 1 - 3 x)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$x + 11 = {(- 1 - 3 x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x + 11 = {(- 1 - 3 x)}^{\frac{2}{2}}$

Rewrite the expression.

$x + 11 = {(- 1 - 3 x)}^{1}$

Simplify.

$x + 11 = - 1 - 3 x$

Step 3

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Add $3 x$ to both sides of the equation.

$x + 11 + 3 x = - 1$

Add $x$ and $3 x$ .

$4 x + 11 = - 1$

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

Subtract $11$ from both sides of the equation.

$4 x = - 1 - 11$

Subtract $11$ from $- 1$ .

$4 x = - 12$

Divide each term in $4 x = - 12$ by $4$ and simplify.

Divide each term in $4 x = - 12$ by $4$ .

$\frac{4 x}{4} = \frac{- 12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 12}{4}$

Divide $x$ by $1$ .

$x = \frac{- 12}{4}$

Simplify the right side.

Divide $- 12$ by $4$ .

$x = - 3$

Solve for x square root of x+11 = square root of -1-3x

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