Solve -1/5a^2-1/125=0

$$- \frac { 1 } { 5 } a ^ { 2 } - \frac { 1 } { 125 } = 0$$

Solve for a

$$a=-\frac{1}{5}i=-0.2i$$

$$a=\frac{1}{5}i=0.2i$$

Steps by Finding Square Root

Add \frac{1}{125} to both sides. Anything plus zero gives itself.

$$-\frac{1}{5}a^{2}=\frac{1}{125}$$

Multiply both sides by -5, the reciprocal of -\frac{1}{5}.

$$a^{2}=\frac{1}{125}\left(-5\right)$$

Multiply \frac{1}{125} and -5 to get -\frac{1}{25}.

$$a^{2}=-\frac{1}{25}$$

The equation is now solved.

$$a=\frac{1}{5}i a=-\frac{1}{5}i$$

Steps Using the Quadratic Formula

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.

$$-\frac{1}{5}a^{2}-\frac{1}{125}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{5} for a, 0 for b, and -\frac{1}{125} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{5}\right)\left(-\frac{1}{125}\right)}}{2\left(-\frac{1}{5}\right)}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{1}{5}\right)\left(-\frac{1}{125}\right)}}{2\left(-\frac{1}{5}\right)}$$

Multiply -4 times -\frac{1}{5}.

$$a=\frac{0±\sqrt{\frac{4}{5}\left(-\frac{1}{125}\right)}}{2\left(-\frac{1}{5}\right)}$$

Multiply \frac{4}{5} times -\frac{1}{125} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$a=\frac{0±\sqrt{-\frac{4}{625}}}{2\left(-\frac{1}{5}\right)}$$

Take the square root of -\frac{4}{625}.

$$a=\frac{0±\frac{2}{25}i}{2\left(-\frac{1}{5}\right)}$$

Multiply 2 times -\frac{1}{5}.

$$a=\frac{0±\frac{2}{25}i}{-\frac{2}{5}}$$

Now solve the equation a=\frac{0±\frac{2}{25}i}{-\frac{2}{5}} when ± is plus.

$$a=-\frac{1}{5}i$$

Now solve the equation a=\frac{0±\frac{2}{25}i}{-\frac{2}{5}} when ± is minus.

$$a=\frac{1}{5}i$$

The equation is now solved.

$$a=-\frac{1}{5}i a=\frac{1}{5}i$$