Solve 2x^2+71=-163

$$2 x ^ { 2 } + 71 = - 163$$

Solve for x (complex solution)

$$x=-3\sqrt{13}i\approx -0-10.816653826i$$

$$x=3\sqrt{13}i\approx 10.816653826i$$

Steps by Finding Square Root

Subtract 71 from both sides.

$$2x^{2}=-163-71$$

Subtract 71 from -163 to get -234.

$$2x^{2}=-234$$

Divide both sides by 2.

$$x^{2}=\frac{-234}{2}$$

Divide -234 by 2 to get -117.

$$x^{2}=-117$$

The equation is now solved.

$$x=3\sqrt{13}i x=-3\sqrt{13}i$$

Steps Using the Quadratic Formula

Add 163 to both sides.

$$2x^{2}+71+163=0$$

Add 71 and 163 to get 234.

$$2x^{2}+234=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 234 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 234}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 234}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 234}}{2\times 2}$$

Multiply -8 times 234.

$$x=\frac{0±\sqrt{-1872}}{2\times 2}$$

Take the square root of -1872.

$$x=\frac{0±12\sqrt{13}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±12\sqrt{13}i}{4}$$

Now solve the equation x=\frac{0±12\sqrt{13}i}{4} when ± is plus.

$$x=3\sqrt{13}i$$

Now solve the equation x=\frac{0±12\sqrt{13}i}{4} when ± is minus.

$$x=-3\sqrt{13}i$$

The equation is now solved.

$$x=3\sqrt{13}i x=-3\sqrt{13}i$$