Solve 1/m^2-2=5

$$\frac { 1 } { m ^ { 2 } } - 2 = 5$$

Solve for m

$$m=\frac{\sqrt{7}}{7}\approx 0.377964473$$

$$m=-\frac{\sqrt{7}}{7}\approx -0.377964473$$

Steps by Finding Square Root

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by m^{2}.

$$1+m^{2}\left(-2\right)=5m^{2}$$

Subtract 5m^{2} from both sides.

$$1+m^{2}\left(-2\right)-5m^{2}=0$$

Combine m^{2}\left(-2\right) and -5m^{2} to get -7m^{2}.

$$1-7m^{2}=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-7m^{2}=-1$$

Divide both sides by -7.

$$m^{2}=\frac{-1}{-7}$$

Fraction \frac{-1}{-7} can be simplified to \frac{1}{7} by removing the negative sign from both the numerator and the denominator.

$$m^{2}=\frac{1}{7}$$

Take the square root of both sides of the equation.

$$m=\frac{\sqrt{7}}{7} m=-\frac{\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by m^{2}.

$$1+m^{2}\left(-2\right)=5m^{2}$$

Subtract 5m^{2} from both sides.

$$1+m^{2}\left(-2\right)-5m^{2}=0$$

Combine m^{2}\left(-2\right) and -5m^{2} to get -7m^{2}.

$$1-7m^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-7m^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -7 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-7\right)}}{2\left(-7\right)}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-7\right)}}{2\left(-7\right)}$$

Multiply -4 times -7.

$$m=\frac{0±\sqrt{28}}{2\left(-7\right)}$$

Take the square root of 28.

$$m=\frac{0±2\sqrt{7}}{2\left(-7\right)}$$

Multiply 2 times -7.

$$m=\frac{0±2\sqrt{7}}{-14}$$

Now solve the equation m=\frac{0±2\sqrt{7}}{-14} when ± is plus.

$$m=-\frac{\sqrt{7}}{7}$$

Now solve the equation m=\frac{0±2\sqrt{7}}{-14} when ± is minus.

$$m=\frac{\sqrt{7}}{7}$$

The equation is now solved.

$$m=-\frac{\sqrt{7}}{7} m=\frac{\sqrt{7}}{7}$$