Solve 2x^2+90=102-78

$$2 x ^ { 2 } + 90 = 102 - 78$$

Solve for x (complex solution)

$$x=-\sqrt{33}i\approx -0-5.744562647i$$

$$x=\sqrt{33}i\approx 5.744562647i$$

Steps by Finding Square Root

Subtract 78 from 102 to get 24.

$$2x^{2}+90=24$$

Subtract 90 from both sides.

$$2x^{2}=24-90$$

Subtract 90 from 24 to get -66.

$$2x^{2}=-66$$

Divide both sides by 2.

$$x^{2}=\frac{-66}{2}$$

Divide -66 by 2 to get -33.

$$x^{2}=-33$$

The equation is now solved.

$$x=\sqrt{33}i x=-\sqrt{33}i$$

Steps Using the Quadratic Formula

Subtract 78 from 102 to get 24.

$$2x^{2}+90=24$$

Subtract 24 from both sides.

$$2x^{2}+90-24=0$$

Subtract 24 from 90 to get 66.

$$2x^{2}+66=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 66 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 66}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 66}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 66}}{2\times 2}$$

Multiply -8 times 66.

$$x=\frac{0±\sqrt{-528}}{2\times 2}$$

Take the square root of -528.

$$x=\frac{0±4\sqrt{33}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{33}i}{4}$$

Now solve the equation x=\frac{0±4\sqrt{33}i}{4} when ± is plus.

$$x=\sqrt{33}i$$

Now solve the equation x=\frac{0±4\sqrt{33}i}{4} when ± is minus.

$$x=-\sqrt{33}i$$

The equation is now solved.

$$x=\sqrt{33}i x=-\sqrt{33}i$$