Solve m^2+25/4=125

$$m ^ { 2 } + \frac { 25 } { 4 } = 125$$

Solve for m

$$m = \frac{5 \sqrt{19}}{2} \approx 10.897247359$$

$$m = -\frac{5 \sqrt{19}}{2} \approx -10.897247359$$

Steps by Finding Square Root

Subtract \frac{25}{4} from both sides.

$$m^{2}=125-\frac{25}{4}$$

Subtract \frac{25}{4} from 125 to get \frac{475}{4}.

$$m^{2}=\frac{475}{4}$$

Take the square root of both sides of the equation.

$$m=\frac{5\sqrt{19}}{2} m=-\frac{5\sqrt{19}}{2}$$

Steps Using the Quadratic Formula

Subtract 125 from both sides.

$$m^{2}+\frac{25}{4}-125=0$$

Subtract 125 from \frac{25}{4} to get -\frac{475}{4}.

$$m^{2}-\frac{475}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{475}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-\frac{475}{4}\right)}}{2}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-\frac{475}{4}\right)}}{2}$$

Multiply -4 times -\frac{475}{4}.

$$m=\frac{0±\sqrt{475}}{2}$$

Take the square root of 475.

$$m=\frac{0±5\sqrt{19}}{2}$$

Now solve the equation m=\frac{0±5\sqrt{19}}{2} when ± is plus.

$$m=\frac{5\sqrt{19}}{2}$$

Now solve the equation m=\frac{0±5\sqrt{19}}{2} when ± is minus.

$$m=-\frac{5\sqrt{19}}{2}$$

The equation is now solved.

$$m=\frac{5\sqrt{19}}{2} m=-\frac{5\sqrt{19}}{2}$$