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

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

Solve for n

$$n=8\sqrt{2}\approx 11.313708499$$

$$n=-8\sqrt{2}\approx -11.313708499$$

Steps by Finding Square Root

Multiply both sides of the equation by 8.

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

Multiply -\frac{n}{8} and -\frac{n}{8} to get \left(-\frac{n}{8}\right)^{2}.

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

Calculate -\frac{n}{8} to the power of 2 and get \left(\frac{n}{8}\right)^{2}.

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

To raise \frac{n}{8} to a power, raise both numerator and denominator to the power and then divide.

$$8\times \frac{n^{2}}{8^{2}}=16$$

Express 8\times \frac{n^{2}}{8^{2}} as a single fraction.

$$\frac{8n^{2}}{8^{2}}=16$$

Cancel out 8 in both numerator and denominator.

$$\frac{n^{2}}{8}=16$$

Multiply both sides by 8.

$$n^{2}=16\times 8$$

Multiply 16 and 8 to get 128.

$$n^{2}=128$$

Take the square root of both sides of the equation.

$$n=8\sqrt{2} n=-8\sqrt{2}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 8.

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

Multiply -\frac{n}{8} and -\frac{n}{8} to get \left(-\frac{n}{8}\right)^{2}.

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

Calculate -\frac{n}{8} to the power of 2 and get \left(\frac{n}{8}\right)^{2}.

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

To raise \frac{n}{8} to a power, raise both numerator and denominator to the power and then divide.

$$8\times \frac{n^{2}}{8^{2}}=16$$

Express 8\times \frac{n^{2}}{8^{2}} as a single fraction.

$$\frac{8n^{2}}{8^{2}}=16$$

Cancel out 8 in both numerator and denominator.

$$\frac{n^{2}}{8}=16$$

Subtract 16 from both sides.

$$\frac{n^{2}}{8}-16=0$$

Multiply both sides of the equation by 8.

$$n^{2}-128=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -128 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-128\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-128\right)}}{2}$$

Multiply -4 times -128.

$$n=\frac{0±\sqrt{512}}{2}$$

Take the square root of 512.

$$n=\frac{0±16\sqrt{2}}{2}$$

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

$$n=8\sqrt{2}$$

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

$$n=-8\sqrt{2}$$

The equation is now solved.

$$n=8\sqrt{2} n=-8\sqrt{2}$$