Solve x^2+5x^2+3=0

$${ x }^{ 2 } +5 { x }^{ 2 } +3=0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2}i}{2}\approx -0-0.707106781i$$

$$x=\frac{\sqrt{2}i}{2}\approx 0.707106781i$$

Steps by Finding Square Root

Combine x^{2} and 5x^{2} to get 6x^{2}.

$$6x^{2}+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$6x^{2}=-3$$

Divide both sides by 6.

$$x^{2}=\frac{-3}{6}$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Combine x^{2} and 5x^{2} to get 6x^{2}.

$$6x^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 3}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\times 3}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\times 3}}{2\times 6}$$

Multiply -24 times 3.

$$x=\frac{0±\sqrt{-72}}{2\times 6}$$

Take the square root of -72.

$$x=\frac{0±6\sqrt{2}i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±6\sqrt{2}i}{12}$$

Now solve the equation x=\frac{0±6\sqrt{2}i}{12} when ± is plus.

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

Now solve the equation x=\frac{0±6\sqrt{2}i}{12} when ± is minus.

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

The equation is now solved.

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