Solve 68=m^2+4m^2

$$68 = m ^ { 2 } + 4 m ^ { 2 }$$

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

Combine m^{2} and 4m^{2} to get 5m^{2}.

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

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

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

Divide both sides by 5.

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

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

Combine m^{2} and 4m^{2} to get 5m^{2}.

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

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

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

Subtract 68 from both sides.

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

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

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

Square 0.

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

Multiply -4 times 5.

$$m=\frac{0±\sqrt{-20\left(-68\right)}}{2\times 5}$$

Multiply -20 times -68.

$$m=\frac{0±\sqrt{1360}}{2\times 5}$$

Take the square root of 1360.

$$m=\frac{0±4\sqrt{85}}{2\times 5}$$

Multiply 2 times 5.

$$m=\frac{0±4\sqrt{85}}{10}$$

Now solve the equation m=\frac{0±4\sqrt{85}}{10} when ± is plus.

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

Now solve the equation m=\frac{0±4\sqrt{85}}{10} when ± is minus.

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

The equation is now solved.

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