Solve x^2=2x^2+1

$${ x }^{ 2 } =2 { x }^{ 2 } +1$$

Solve for x (complex solution)

$$x=-i$$

$$x=i$$

Steps by Finding Square Root

Subtract 2x^{2} from both sides.

$$x^{2}-2x^{2}=1$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}=1$$

Divide both sides by -1.

$$x^{2}=-1$$

The equation is now solved.

$$x=i x=-i$$

Steps Using the Quadratic Formula

Subtract 2x^{2} from both sides.

$$x^{2}-2x^{2}=1$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}=1$$

Subtract 1 from both sides.

$$-x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-1\right)}}{2\left(-1\right)}$$

Multiply 4 times -1.

$$x=\frac{0±\sqrt{-4}}{2\left(-1\right)}$$

Take the square root of -4.

$$x=\frac{0±2i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2i}{-2}$$

Now solve the equation x=\frac{0±2i}{-2} when ± is plus.

$$x=-i$$

Now solve the equation x=\frac{0±2i}{-2} when ± is minus.

$$x=i$$

The equation is now solved.

$$x=-i x=i$$