Solve [510/8*-80)m^2=60

$$[ \frac { 510 } { 8 \cdot - 80 } ) m ^ { 2 } = 60$$

Solve for m

$$m=-\frac{16\sqrt{85}i}{17}\approx -0-8.677218313i$$

$$m=\frac{16\sqrt{85}i}{17}\approx 8.677218313i$$

Steps by Finding Square Root

Multiply 8 and -80 to get -640.

$$\frac{510}{-640}m^{2}=60$$

Reduce the fraction \frac{510}{-640} to lowest terms by extracting and canceling out 10.

$$-\frac{51}{64}m^{2}=60$$

Multiply both sides by -\frac{64}{51}, the reciprocal of -\frac{51}{64}.

$$m^{2}=60\left(-\frac{64}{51}\right)$$

Multiply 60 and -\frac{64}{51} to get -\frac{1280}{17}.

$$m^{2}=-\frac{1280}{17}$$

The equation is now solved.

$$m=\frac{16\sqrt{85}i}{17} m=-\frac{16\sqrt{85}i}{17}$$

Steps Using the Quadratic Formula

Multiply 8 and -80 to get -640.

$$\frac{510}{-640}m^{2}=60$$

Reduce the fraction \frac{510}{-640} to lowest terms by extracting and canceling out 10.

$$-\frac{51}{64}m^{2}=60$$

Subtract 60 from both sides.

$$-\frac{51}{64}m^{2}-60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{51}{64} for a, 0 for b, and -60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-\frac{51}{64}\right)\left(-60\right)}}{2\left(-\frac{51}{64}\right)}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-\frac{51}{64}\right)\left(-60\right)}}{2\left(-\frac{51}{64}\right)}$$

Multiply -4 times -\frac{51}{64}.

$$m=\frac{0±\sqrt{\frac{51}{16}\left(-60\right)}}{2\left(-\frac{51}{64}\right)}$$

Multiply \frac{51}{16} times -60.

$$m=\frac{0±\sqrt{-\frac{765}{4}}}{2\left(-\frac{51}{64}\right)}$$

Take the square root of -\frac{765}{4}.

$$m=\frac{0±\frac{3\sqrt{85}i}{2}}{2\left(-\frac{51}{64}\right)}$$

Multiply 2 times -\frac{51}{64}.

$$m=\frac{0±\frac{3\sqrt{85}i}{2}}{-\frac{51}{32}}$$

Now solve the equation m=\frac{0±\frac{3\sqrt{85}i}{2}}{-\frac{51}{32}} when ± is plus.

$$m=-\frac{16\sqrt{85}i}{17}$$

Now solve the equation m=\frac{0±\frac{3\sqrt{85}i}{2}}{-\frac{51}{32}} when ± is minus.

$$m=\frac{16\sqrt{85}i}{17}$$

The equation is now solved.

$$m=-\frac{16\sqrt{85}i}{17} m=\frac{16\sqrt{85}i}{17}$$