Solve x^2=5x^2+6

$${ x }^{ 2 } =5 { x }^{ 2 } +6$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{6}i}{2}\approx -0-1.224744871i$$

$$x=\frac{\sqrt{6}i}{2}\approx 1.224744871i$$

Steps by Finding Square Root

Subtract 5x^{2} from both sides.

$$x^{2}-5x^{2}=6$$

Combine x^{2} and -5x^{2} to get -4x^{2}.

$$-4x^{2}=6$$

Divide both sides by -4.

$$x^{2}=\frac{6}{-4}$$

Reduce the fraction \frac{6}{-4} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{3}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{6}i}{2} x=-\frac{\sqrt{6}i}{2}$$

Steps Using the Quadratic Formula

Subtract 5x^{2} from both sides.

$$x^{2}-5x^{2}=6$$

Combine x^{2} and -5x^{2} to get -4x^{2}.

$$-4x^{2}=6$$

Subtract 6 from both sides.

$$-4x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\left(-6\right)}}{2\left(-4\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\left(-6\right)}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\left(-6\right)}}{2\left(-4\right)}$$

Multiply 16 times -6.

$$x=\frac{0±\sqrt{-96}}{2\left(-4\right)}$$

Take the square root of -96.

$$x=\frac{0±4\sqrt{6}i}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±4\sqrt{6}i}{-8}$$

Now solve the equation x=\frac{0±4\sqrt{6}i}{-8} when ± is plus.

$$x=-\frac{\sqrt{6}i}{2}$$

Now solve the equation x=\frac{0±4\sqrt{6}i}{-8} when ± is minus.

$$x=\frac{\sqrt{6}i}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{6}i}{2} x=\frac{\sqrt{6}i}{2}$$