Solve for x (-3-x)^(1/2)=(3x+17)^(1/2)

${(- 3 - x)}^{\frac{1}{2}} = {(3 x + 17)}^{\frac{1}{2}}$

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$- 3 - x = 3 x + 17$

Solve for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$- 3 - x - 3 x = 17$

Subtract $3 x$ from $- x$ .

$- 3 - 4 x = 17$

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

Add $3$ to both sides of the equation.

$- 4 x = 17 + 3$

Add $17$ and $3$ .

$- 4 x = 20$

Divide each term in $- 4 x = 20$ by $- 4$ and simplify.

Divide each term in $- 4 x = 20$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{20}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{20}{- 4}$

Divide $x$ by $1$ .

$x = \frac{20}{- 4}$

Simplify the right side.

Divide $20$ by $- 4$ .

$x = - 5$