Solve x=3sqrt{-x}

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

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(3\sqrt{-x}\right)^{2}$$

Expand \left(3\sqrt{-x}\right)^{2}.

$$x^{2}=3^{2}\left(\sqrt{-x}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=9\left(\sqrt{-x}\right)^{2}$$

Calculate \sqrt{-x} to the power of 2 and get -x.

$$x^{2}=9\left(-x\right)$$

Subtract 9\left(-x\right) from both sides.

$$x^{2}-9\left(-x\right)=0$$

Multiply -1 and 9 to get -9.

$$x^{2}-9\left(-1\right)x=0$$

Multiply -9 and -1 to get 9.

$$x^{2}+9x=0$$

Factor out x.

$$x\left(x+9\right)=0$$

To find equation solutions, solve x=0 and x+9=0.

$$x=0 x=-9$$

Substitute 0 for x in the equation x=3\sqrt{-x}.

$$0=3\sqrt{0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute -9 for x in the equation x=3\sqrt{-x}.

$$-9=3\sqrt{-\left(-9\right)}$$

Simplify. The value x=-9 does not satisfy the equation because the left and the right hand side have opposite signs.

$$-9=9$$

Equation x=3\sqrt{-x} has a unique solution.

$$x=0$$