Solve -1/5x^2+20=0

$$- \frac{ 1 }{ 5 } { x }^{ 2 } +20 = 0$$

Solve for x

$$x=10$$

$$x=-10$$

Steps by Finding Square Root

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{5}x^{2}=-20$$

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

$$x^{2}=-20\left(-5\right)$$

Multiply -20 and -5 to get 100.

$$x^{2}=100$$

Take the square root of both sides of the equation.

$$x=10 x=-10$$

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.

$$-\frac{1}{5}x^{2}+20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{5} for a, 0 for b, and 20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{5}\right)\times 20}}{2\left(-\frac{1}{5}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{5}\right)\times 20}}{2\left(-\frac{1}{5}\right)}$$

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

$$x=\frac{0±\sqrt{\frac{4}{5}\times 20}}{2\left(-\frac{1}{5}\right)}$$

Multiply \frac{4}{5} times 20.

$$x=\frac{0±\sqrt{16}}{2\left(-\frac{1}{5}\right)}$$

Take the square root of 16.

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

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

$$x=\frac{0±4}{-\frac{2}{5}}$$

Now solve the equation x=\frac{0±4}{-\frac{2}{5}} when ± is plus. Divide 4 by -\frac{2}{5} by multiplying 4 by the reciprocal of -\frac{2}{5}.

$$x=-10$$

Now solve the equation x=\frac{0±4}{-\frac{2}{5}} when ± is minus. Divide -4 by -\frac{2}{5} by multiplying -4 by the reciprocal of -\frac{2}{5}.

$$x=10$$

The equation is now solved.

$$x=-10 x=10$$