Solve 3sqrt{3x}+4sqrt{2x}=0

$$3 \sqrt { 3 x } + 4 \sqrt { 2 x } = 0$$

Solve for x

$$x=0$$

Solution Steps

Subtract 4\sqrt{2x} from both sides of the equation.

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

Square both sides of the equation.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

Multiply 9 and 3 to get 27.

$$27x=\left(-4\sqrt{2x}\right)^{2}$$

Expand \left(-4\sqrt{2x}\right)^{2}.

$$27x=\left(-4\right)^{2}\left(\sqrt{2x}\right)^{2}$$

Calculate -4 to the power of 2 and get 16.

$$27x=16\left(\sqrt{2x}\right)^{2}$$

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

$$27x=16\times 2x$$

Multiply 16 and 2 to get 32.

$$27x=32x$$

Subtract 32x from both sides.

$$27x-32x=0$$

Combine 27x and -32x to get -5x.

$$-5x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -5 is not equal to 0, x must be equal to 0.

$$x=0$$

Substitute 0 for x in the equation 3\sqrt{3x}+4\sqrt{2x}=0.

$$3\sqrt{3\times 0}+4\sqrt{2\times 0}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

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

$$x=0$$