Solve 2n^2=-144

$$2 n ^ { 2 } = - 144$$

Solve for n

$$n=-6\sqrt{2}i\approx -0-8.485281374i$$

$$n=6\sqrt{2}i\approx 8.485281374i$$

Steps by Finding Square Root

Divide both sides by 2.

$$n^{2}=\frac{-144}{2}$$

Divide -144 by 2 to get -72.

$$n^{2}=-72$$

The equation is now solved.

$$n=6\sqrt{2}i n=-6\sqrt{2}i$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$n^{2}=\frac{-144}{2}$$

Divide -144 by 2 to get -72.

$$n^{2}=-72$$

Add 72 to both sides.

$$n^{2}+72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 72}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 72}}{2}$$

Multiply -4 times 72.

$$n=\frac{0±\sqrt{-288}}{2}$$

Take the square root of -288.

$$n=\frac{0±12\sqrt{2}i}{2}$$

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

$$n=6\sqrt{2}i$$

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

$$n=-6\sqrt{2}i$$

The equation is now solved.

$$n=6\sqrt{2}i n=-6\sqrt{2}i$$