Solve 78x^2+3=0

$$78 { x }^{ 2 } +3=0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{26}i}{26}\approx -0-0.196116135i$$

$$x=\frac{\sqrt{26}i}{26}\approx 0.196116135i$$

Steps by Finding Square Root

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

$$78x^{2}=-3$$

Divide both sides by 78.

$$x^{2}=\frac{-3}{78}$$

Reduce the fraction \frac{-3}{78} to lowest terms by extracting and canceling out 3.

$$x^{2}=-\frac{1}{26}$$

The equation is now solved.

$$x=\frac{\sqrt{26}i}{26} x=-\frac{\sqrt{26}i}{26}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$78x^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 78 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 78\times 3}}{2\times 78}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 78\times 3}}{2\times 78}$$

Multiply -4 times 78.

$$x=\frac{0±\sqrt{-312\times 3}}{2\times 78}$$

Multiply -312 times 3.

$$x=\frac{0±\sqrt{-936}}{2\times 78}$$

Take the square root of -936.

$$x=\frac{0±6\sqrt{26}i}{2\times 78}$$

Multiply 2 times 78.

$$x=\frac{0±6\sqrt{26}i}{156}$$

Now solve the equation x=\frac{0±6\sqrt{26}i}{156} when ± is plus.

$$x=\frac{\sqrt{26}i}{26}$$

Now solve the equation x=\frac{0±6\sqrt{26}i}{156} when ± is minus.

$$x=-\frac{\sqrt{26}i}{26}$$

The equation is now solved.

$$x=\frac{\sqrt{26}i}{26} x=-\frac{\sqrt{26}i}{26}$$