Solve -1/10x^2+20=1/10x^2-20

$$- \frac{ 1 }{ 10 } { x }^{ 2 } +20 = \frac{ 1 }{ 10 } { x }^{ 2 } -20$$

Solve for x

$$x=10\sqrt{2}\approx 14.142135624$$

$$x=-10\sqrt{2}\approx -14.142135624$$

Steps by Finding Square Root

Subtract \frac{1}{10}x^{2} from both sides.

$$-\frac{1}{10}x^{2}+20-\frac{1}{10}x^{2}=-20$$

Combine -\frac{1}{10}x^{2} and -\frac{1}{10}x^{2} to get -\frac{1}{5}x^{2}.

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

Subtract 20 from both sides.

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

Subtract 20 from -20 to get -40.

$$-\frac{1}{5}x^{2}=-40$$

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

$$x^{2}=-40\left(-5\right)$$

Multiply -40 and -5 to get 200.

$$x^{2}=200$$

Take the square root of both sides of the equation.

$$x=10\sqrt{2} x=-10\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract \frac{1}{10}x^{2} from both sides.

$$-\frac{1}{10}x^{2}+20-\frac{1}{10}x^{2}=-20$$

Combine -\frac{1}{10}x^{2} and -\frac{1}{10}x^{2} to get -\frac{1}{5}x^{2}.

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

Add 20 to both sides.

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

Add 20 and 20 to get 40.

$$-\frac{1}{5}x^{2}+40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{5} for a, 0 for b, and 40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{5}\right)\times 40}}{2\left(-\frac{1}{5}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{5}\right)\times 40}}{2\left(-\frac{1}{5}\right)}$$

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

$$x=\frac{0±\sqrt{\frac{4}{5}\times 40}}{2\left(-\frac{1}{5}\right)}$$

Multiply \frac{4}{5} times 40.

$$x=\frac{0±\sqrt{32}}{2\left(-\frac{1}{5}\right)}$$

Take the square root of 32.

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

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

$$x=\frac{0±4\sqrt{2}}{-\frac{2}{5}}$$

Now solve the equation x=\frac{0±4\sqrt{2}}{-\frac{2}{5}} when ± is plus.

$$x=-10\sqrt{2}$$

Now solve the equation x=\frac{0±4\sqrt{2}}{-\frac{2}{5}} when ± is minus.

$$x=10\sqrt{2}$$

The equation is now solved.

$$x=-10\sqrt{2} x=10\sqrt{2}$$