Solve sqrt{x^2+a}=2x

$$\sqrt{ { x }^{ 2 } +a } = 2x$$

Solve for a

$$a=3x^{2}$$

$$x\geq 0$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$a+x^{2}=4x^{2}$$

Subtract x^{2} from both sides of the equation.

$$a+x^{2}-x^{2}=4x^{2}-x^{2}$$

Subtracting x^{2} from itself leaves 0.

$$a=4x^{2}-x^{2}$$

Subtract x^{2} from 4x^{2}.

$$a=3x^{2}$$

Solve for a (complex solution)

$$a=3x^{2}$$

$$arg(x)<\pi \text{ or }x=0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{3a}}{3}$$

Solve for x

$$x=\frac{\sqrt{3a}}{3}$$

$$a\geq 0$$