Solve x=sqrt{x*102*2^2}

$$x= \sqrt{ x \times 102 \times { 2 }^{ 2 } }$$

Solve for x

$$x=408$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(\sqrt{x\times 102\times 2^{2}}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}=\left(\sqrt{x\times 102\times 4}\right)^{2}$$

Multiply 102 and 4 to get 408.

$$x^{2}=\left(\sqrt{x\times 408}\right)^{2}$$

Calculate \sqrt{x\times 408} to the power of 2 and get x\times 408.

$$x^{2}=x\times 408$$

Subtract x\times 408 from both sides.

$$x^{2}-x\times 408=0$$

Multiply -1 and 408 to get -408.

$$x^{2}-408x=0$$

Factor out x.

$$x\left(x-408\right)=0$$

To find equation solutions, solve x=0 and x-408=0.

$$x=0 x=408$$

Substitute 0 for x in the equation x=\sqrt{x\times 102\times 2^{2}}.

$$0=\sqrt{0\times 102\times 2^{2}}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 408 for x in the equation x=\sqrt{x\times 102\times 2^{2}}.

$$408=\sqrt{408\times 102\times 2^{2}}$$

Simplify. The value x=408 satisfies the equation.

$$408=408$$

List all solutions of x=\sqrt{408x}.

$$x=0 x=408$$