Solve 125(m)^2=180

$$125 ( m ) ^ { 2 } = 180$$

Solve for m

$$m = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

$$m = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps Using Difference of Squares

Divide both sides by 125.

$$m^{2}=\frac{180}{125}$$

Reduce the fraction \frac{180}{125} to lowest terms by extracting and canceling out 5.

$$m^{2}=\frac{36}{25}$$

Subtract \frac{36}{25} from both sides.

$$m^{2}-\frac{36}{25}=0$$

Multiply both sides by 25.

$$25m^{2}-36=0$$

Consider 25m^{2}-36. Rewrite 25m^{2}-36 as \left(5m\right)^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5m-6\right)\left(5m+6\right)=0$$

To find equation solutions, solve 5m-6=0 and 5m+6=0.

$$m=\frac{6}{5} m=-\frac{6}{5}$$

Steps by Finding Square Root

Divide both sides by 125.

$$m^{2}=\frac{180}{125}$$

Reduce the fraction \frac{180}{125} to lowest terms by extracting and canceling out 5.

$$m^{2}=\frac{36}{25}$$

Take the square root of both sides of the equation.

$$m=\frac{6}{5} m=-\frac{6}{5}$$

Steps Using the Quadratic Formula

Divide both sides by 125.

$$m^{2}=\frac{180}{125}$$

Reduce the fraction \frac{180}{125} to lowest terms by extracting and canceling out 5.

$$m^{2}=\frac{36}{25}$$

Subtract \frac{36}{25} from both sides.

$$m^{2}-\frac{36}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{36}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-\frac{36}{25}\right)}}{2}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-\frac{36}{25}\right)}}{2}$$

Multiply -4 times -\frac{36}{25}.

$$m=\frac{0±\sqrt{\frac{144}{25}}}{2}$$

Take the square root of \frac{144}{25}.

$$m=\frac{0±\frac{12}{5}}{2}$$

Now solve the equation m=\frac{0±\frac{12}{5}}{2} when ± is plus.

$$m=\frac{6}{5}$$

Now solve the equation m=\frac{0±\frac{12}{5}}{2} when ± is minus.

$$m=-\frac{6}{5}$$

The equation is now solved.

$$m=\frac{6}{5} m=-\frac{6}{5}$$