Solve (-n/8)(n+n/8)=2

$$( - \frac { n } { 8 } ) ( \frac { n + n } { 8 } ) = 2$$

Solve for n

$$n=-8i$$

$$n=8i$$

Steps by Finding Square Root

Multiply both sides of the equation by 8.

$$\left(-\frac{n}{8}\right)\left(n+n\right)=16$$

Combine n and n to get 2n.

$$\left(-\frac{n}{8}\right)\times 2n=16$$

Cancel out 8, the greatest common factor in 2 and 8.

$$\frac{n}{-4}n=16$$

Express \frac{n}{-4}n as a single fraction.

$$\frac{nn}{-4}=16$$

Multiply n and n to get n^{2}.

$$\frac{n^{2}}{-4}=16$$

Multiply both sides by -4.

$$n^{2}=16\left(-4\right)$$

Multiply 16 and -4 to get -64.

$$n^{2}=-64$$

The equation is now solved.

$$n=8i n=-8i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 8.

$$\left(-\frac{n}{8}\right)\left(n+n\right)=16$$

Combine n and n to get 2n.

$$\left(-\frac{n}{8}\right)\times 2n=16$$

Cancel out 8, the greatest common factor in 2 and 8.

$$\frac{n}{-4}n=16$$

Express \frac{n}{-4}n as a single fraction.

$$\frac{nn}{-4}=16$$

Multiply n and n to get n^{2}.

$$\frac{n^{2}}{-4}=16$$

Subtract 16 from both sides.

$$\frac{n^{2}}{-4}-16=0$$

Multiply both sides of the equation by -4.

$$n^{2}+64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 64}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 64}}{2}$$

Multiply -4 times 64.

$$n=\frac{0±\sqrt{-256}}{2}$$

Take the square root of -256.

$$n=\frac{0±16i}{2}$$

Now solve the equation n=\frac{0±16i}{2} when ± is plus.

$$n=8i$$

Now solve the equation n=\frac{0±16i}{2} when ± is minus.

$$n=-8i$$

The equation is now solved.

$$n=8i n=-8i$$