Solve .2=1-1/k^2

$$.2 = 1 - \frac { 1 } { k ^ { 2 } }$$

Solve for k

$$k = \frac{\sqrt{5}}{2} \approx 1.118033989$$

$$k = -\frac{\sqrt{5}}{2} \approx -1.118033989$$

Steps by Finding Square Root

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

$$0.2k^{2}=k^{2}-1$$

Subtract k^{2} from both sides.

$$0.2k^{2}-k^{2}=-1$$

Combine 0.2k^{2} and -k^{2} to get -0.8k^{2}.

$$-0.8k^{2}=-1$$

Divide both sides by -0.8.

$$k^{2}=\frac{-1}{-0.8}$$

Expand \frac{-1}{-0.8} by multiplying both numerator and the denominator by 10.

$$k^{2}=\frac{-10}{-8}$$

Reduce the fraction \frac{-10}{-8} to lowest terms by extracting and canceling out -2.

$$k^{2}=\frac{5}{4}$$

Take the square root of both sides of the equation.

$$k=\frac{\sqrt{5}}{2} k=-\frac{\sqrt{5}}{2}$$

Steps Using the Quadratic Formula

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

$$0.2k^{2}=k^{2}-1$$

Subtract k^{2} from both sides.

$$0.2k^{2}-k^{2}=-1$$

Combine 0.2k^{2} and -k^{2} to get -0.8k^{2}.

$$-0.8k^{2}=-1$$

Add 1 to both sides.

$$-0.8k^{2}+1=0$$

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.

$$-\frac{4}{5}k^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{4}{5} for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-\frac{4}{5}\right)}}{2\left(-\frac{4}{5}\right)}$$

Square 0.

$$k=\frac{0±\sqrt{-4\left(-\frac{4}{5}\right)}}{2\left(-\frac{4}{5}\right)}$$

Multiply -4 times -\frac{4}{5}.

$$k=\frac{0±\sqrt{\frac{16}{5}}}{2\left(-\frac{4}{5}\right)}$$

Take the square root of \frac{16}{5}.

$$k=\frac{0±\frac{4\sqrt{5}}{5}}{2\left(-\frac{4}{5}\right)}$$

Multiply 2 times -\frac{4}{5}.

$$k=\frac{0±\frac{4\sqrt{5}}{5}}{-\frac{8}{5}}$$

Now solve the equation k=\frac{0±\frac{4\sqrt{5}}{5}}{-\frac{8}{5}} when ± is plus.

$$k=-\frac{\sqrt{5}}{2}$$

Now solve the equation k=\frac{0±\frac{4\sqrt{5}}{5}}{-\frac{8}{5}} when ± is minus.

$$k=\frac{\sqrt{5}}{2}$$

The equation is now solved.

$$k=-\frac{\sqrt{5}}{2} k=\frac{\sqrt{5}}{2}$$