Solve 68=5m^2

$$68 = 5 m ^ { 2 }$$

Solve for m

$$m = \frac{2 \sqrt{85}}{5} \approx 3.687817783$$

$$m = -\frac{2 \sqrt{85}}{5} \approx -3.687817783$$

Steps by Finding Square Root

Divide both sides by 5.

$$\frac{68}{5}=m^{2}$$

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

$$m^{2}=\frac{68}{5}$$

Take the square root of both sides of the equation.

$$m=\frac{2\sqrt{85}}{5} m=-\frac{2\sqrt{85}}{5}$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$\frac{68}{5}=m^{2}$$

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

$$m^{2}=\frac{68}{5}$$

Subtract \frac{68}{5} from both sides.

$$m^{2}-\frac{68}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{68}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-\frac{68}{5}\right)}}{2}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-\frac{68}{5}\right)}}{2}$$

Multiply -4 times -\frac{68}{5}.

$$m=\frac{0±\sqrt{\frac{272}{5}}}{2}$$

Take the square root of \frac{272}{5}.

$$m=\frac{0±\frac{4\sqrt{85}}{5}}{2}$$

Now solve the equation m=\frac{0±\frac{4\sqrt{85}}{5}}{2} when ± is plus.

$$m=\frac{2\sqrt{85}}{5}$$

Now solve the equation m=\frac{0±\frac{4\sqrt{85}}{5}}{2} when ± is minus.

$$m=-\frac{2\sqrt{85}}{5}$$

The equation is now solved.

$$m=\frac{2\sqrt{85}}{5} m=-\frac{2\sqrt{85}}{5}$$