Solve quad[240m^2]=2

$$\quad [ 240 m ^ { 2 } ] = 2$$

Solve for m

$$m=\frac{\sqrt{30}}{60}\approx 0.091287093$$

$$m=-\frac{\sqrt{30}}{60}\approx -0.091287093$$

Steps by Finding Square Root

Divide both sides by 240.

$$m^{2}=\frac{2}{240}$$

Reduce the fraction \frac{2}{240} to lowest terms by extracting and canceling out 2.

$$m^{2}=\frac{1}{120}$$

Take the square root of both sides of the equation.

$$m=\frac{\sqrt{30}}{60} m=-\frac{\sqrt{30}}{60}$$

Steps Using the Quadratic Formula

Divide both sides by 240.

$$m^{2}=\frac{2}{240}$$

Reduce the fraction \frac{2}{240} to lowest terms by extracting and canceling out 2.

$$m^{2}=\frac{1}{120}$$

Subtract \frac{1}{120} from both sides.

$$m^{2}-\frac{1}{120}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{120} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{120}\right)}}{2}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-\frac{1}{120}\right)}}{2}$$

Multiply -4 times -\frac{1}{120}.

$$m=\frac{0±\sqrt{\frac{1}{30}}}{2}$$

Take the square root of \frac{1}{30}.

$$m=\frac{0±\frac{\sqrt{30}}{30}}{2}$$

Now solve the equation m=\frac{0±\frac{\sqrt{30}}{30}}{2} when ± is plus.

$$m=\frac{\sqrt{30}}{60}$$

Now solve the equation m=\frac{0±\frac{\sqrt{30}}{30}}{2} when ± is minus.

$$m=-\frac{\sqrt{30}}{60}$$

The equation is now solved.

$$m=\frac{\sqrt{30}}{60} m=-\frac{\sqrt{30}}{60}$$