Solve for x square root of 2-x = square root of -5-2x

$\sqrt{2 - x} = \sqrt{- 5 - 2 x}$

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

${\sqrt{2 - x}}^{2} = {\sqrt{- 5 - 2 x}}^{2}$

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(2 - x)}^{1} = {\sqrt{- 5 - 2 x}}^{2}$

Simplify.

$2 - x = {\sqrt{- 5 - 2 x}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{- 5 - 2 x}}^{2}$ as $- 5 - 2 x$ .

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$2 - x = - 5 - 2 x$

Solve for $x$ .

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

Add $2 x$ to both sides of the equation.

$2 - x + 2 x = - 5$

Add $- x$ and $2 x$ .

$2 + x = - 5$

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

Subtract $2$ from both sides of the equation.

$x = - 5 - 2$

Subtract $2$ from $- 5$ .

$x = - 7$