Solve 11=6n^2

$$11 = 6 n ^ { 2 }$$

Solve for n

$$n = \frac{\sqrt{66}}{6} \approx 1.354006401$$

$$n = -\frac{\sqrt{66}}{6} \approx -1.354006401$$

Steps by Finding Square Root

Divide both sides by 6.

$$\frac{11}{6}=n^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$n^{2}=\frac{11}{6}$$

Take the square root of both sides of the equation.

$$n=\frac{\sqrt{66}}{6} n=-\frac{\sqrt{66}}{6}$$

Steps Using the Quadratic Formula

Divide both sides by 6.

$$\frac{11}{6}=n^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$n^{2}=\frac{11}{6}$$

Subtract \frac{11}{6} from both sides.

$$n^{2}-\frac{11}{6}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{11}{6} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-\frac{11}{6}\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-\frac{11}{6}\right)}}{2}$$

Multiply -4 times -\frac{11}{6}.

$$n=\frac{0±\sqrt{\frac{22}{3}}}{2}$$

Take the square root of \frac{22}{3}.

$$n=\frac{0±\frac{\sqrt{66}}{3}}{2}$$

Now solve the equation n=\frac{0±\frac{\sqrt{66}}{3}}{2} when ± is plus.

$$n=\frac{\sqrt{66}}{6}$$

Now solve the equation n=\frac{0±\frac{\sqrt{66}}{3}}{2} when ± is minus.

$$n=-\frac{\sqrt{66}}{6}$$

The equation is now solved.

$$n=\frac{\sqrt{66}}{6} n=-\frac{\sqrt{66}}{6}$$