Solve (2x^2+1^2)-4x^2=3x^2+2

$$(2 { x }^{ 2 } + { 1 }^{ 2 } )-4 { x }^{ 2 } =3 { x }^{ 2 } +2$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{5}i}{5}\approx -0-0.447213595i$$

$$x=\frac{\sqrt{5}i}{5}\approx 0.447213595i$$

Steps by Finding Square Root

Calculate 1 to the power of 2 and get 1.

$$2x^{2}+1-4x^{2}=3x^{2}+2$$

Combine 2x^{2} and -4x^{2} to get -2x^{2}.

$$-2x^{2}+1=3x^{2}+2$$

Subtract 3x^{2} from both sides.

$$-2x^{2}+1-3x^{2}=2$$

Combine -2x^{2} and -3x^{2} to get -5x^{2}.

$$-5x^{2}+1=2$$

Subtract 1 from both sides.

$$-5x^{2}=2-1$$

Subtract 1 from 2 to get 1.

$$-5x^{2}=1$$

Divide both sides by -5.

$$x^{2}=-\frac{1}{5}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Calculate 1 to the power of 2 and get 1.

$$2x^{2}+1-4x^{2}=3x^{2}+2$$

Combine 2x^{2} and -4x^{2} to get -2x^{2}.

$$-2x^{2}+1=3x^{2}+2$$

Subtract 3x^{2} from both sides.

$$-2x^{2}+1-3x^{2}=2$$

Combine -2x^{2} and -3x^{2} to get -5x^{2}.

$$-5x^{2}+1=2$$

Subtract 2 from both sides.

$$-5x^{2}+1-2=0$$

Subtract 2 from 1 to get -1.

$$-5x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)\left(-1\right)}}{2\left(-5\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)\left(-1\right)}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{0±\sqrt{20\left(-1\right)}}{2\left(-5\right)}$$

Multiply 20 times -1.

$$x=\frac{0±\sqrt{-20}}{2\left(-5\right)}$$

Take the square root of -20.

$$x=\frac{0±2\sqrt{5}i}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{0±2\sqrt{5}i}{-10}$$

Now solve the equation x=\frac{0±2\sqrt{5}i}{-10} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{5}i}{-10} when ± is minus.

$$x=\frac{\sqrt{5}i}{5}$$

The equation is now solved.

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