Solve 8n^2+72=0

$$8 n ^ { 2 } + 72 = 0$$

Solve for n

$$n=-3i$$

$$n=3i$$

Steps by Finding Square Root

Subtract 72 from both sides. Anything subtracted from zero gives its negation.

$$8n^{2}=-72$$

Divide both sides by 8.

$$n^{2}=\frac{-72}{8}$$

Divide -72 by 8 to get -9.

$$n^{2}=-9$$

The equation is now solved.

$$n=3i n=-3i$$

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.

$$8n^{2}+72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and 72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 8\times 72}}{2\times 8}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 8\times 72}}{2\times 8}$$

Multiply -4 times 8.

$$n=\frac{0±\sqrt{-32\times 72}}{2\times 8}$$

Multiply -32 times 72.

$$n=\frac{0±\sqrt{-2304}}{2\times 8}$$

Take the square root of -2304.

$$n=\frac{0±48i}{2\times 8}$$

Multiply 2 times 8.

$$n=\frac{0±48i}{16}$$

Now solve the equation n=\frac{0±48i}{16} when ± is plus.

$$n=3i$$

Now solve the equation n=\frac{0±48i}{16} when ± is minus.

$$n=-3i$$

The equation is now solved.

$$n=3i n=-3i$$