Solve -2x^2-44=312

$$- 2 x ^ { 2 } - 44 = 312$$

Solve for x (complex solution)

$$x=-\sqrt{178}i\approx -0-13.341664064i$$

$$x=\sqrt{178}i\approx 13.341664064i$$

Steps by Finding Square Root

Add 44 to both sides.

$$-2x^{2}=312+44$$

Add 312 and 44 to get 356.

$$-2x^{2}=356$$

Divide both sides by -2.

$$x^{2}=\frac{356}{-2}$$

Divide 356 by -2 to get -178.

$$x^{2}=-178$$

The equation is now solved.

$$x=\sqrt{178}i x=-\sqrt{178}i$$

Steps Using the Quadratic Formula

Subtract 312 from both sides.

$$-2x^{2}-44-312=0$$

Subtract 312 from -44 to get -356.

$$-2x^{2}-356=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and -356 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\left(-356\right)}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\left(-356\right)}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\left(-356\right)}}{2\left(-2\right)}$$

Multiply 8 times -356.

$$x=\frac{0±\sqrt{-2848}}{2\left(-2\right)}$$

Take the square root of -2848.

$$x=\frac{0±4\sqrt{178}i}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±4\sqrt{178}i}{-4}$$

Now solve the equation x=\frac{0±4\sqrt{178}i}{-4} when ± is plus.

$$x=-\sqrt{178}i$$

Now solve the equation x=\frac{0±4\sqrt{178}i}{-4} when ± is minus.

$$x=\sqrt{178}i$$

The equation is now solved.

$$x=-\sqrt{178}i x=\sqrt{178}i$$