Solve sqrt{-2x-4}=sqrt{-9+3x}

$$\sqrt { - 2 x - 4 } = \sqrt { - 9 + 3 x }$$

Solve for x (complex solution)

$$x=1$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{-2x-4}\right)^{2}=\left(\sqrt{-9+3x}\right)^{2}$$

Calculate \sqrt{-2x-4} to the power of 2 and get -2x-4.

$$-2x-4=\left(\sqrt{-9+3x}\right)^{2}$$

Calculate \sqrt{-9+3x} to the power of 2 and get -9+3x.

$$-2x-4=-9+3x$$

Subtract 3x from both sides.

$$-2x-4-3x=-9$$

Combine -2x and -3x to get -5x.

$$-5x-4=-9$$

Add 4 to both sides.

$$-5x=-9+4$$

Add -9 and 4 to get -5.

$$-5x=-5$$

Divide both sides by -5.

$$x=\frac{-5}{-5}$$

Divide -5 by -5 to get 1.

$$x=1$$

Substitute 1 for x in the equation \sqrt{-2x-4}=\sqrt{-9+3x}.

$$\sqrt{-2-4}=\sqrt{-9+3\times 1}$$

Simplify. The value x=1 satisfies the equation.

$$i\times 6^{\frac{1}{2}}=i\times 6^{\frac{1}{2}}$$

Equation \sqrt{-2x-4}=\sqrt{3x-9} has a unique solution.

$$x=1$$