Solve 1/x-x/100=0

$$\frac { 1 } { x } - \frac { x } { 100 } = 0$$

Solve for x

$$x=10$$

$$x=-10$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100x, the least common multiple of x,100.

$$100-xx=0$$

Multiply x and x to get x^{2}.

$$100-x^{2}=0$$

Subtract 100 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-100$$

Divide both sides by -1.

$$x^{2}=\frac{-100}{-1}$$

Fraction \frac{-100}{-1} can be simplified to 100 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=100$$

Take the square root of both sides of the equation.

$$x=10 x=-10$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100x, the least common multiple of x,100.

$$100-xx=0$$

Multiply x and x to get x^{2}.

$$100-x^{2}=0$$

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.

$$-x^{2}+100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 100}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 100}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 100}}{2\left(-1\right)}$$

Multiply 4 times 100.

$$x=\frac{0±\sqrt{400}}{2\left(-1\right)}$$

Take the square root of 400.

$$x=\frac{0±20}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±20}{-2}$$

Now solve the equation x=\frac{0±20}{-2} when ± is plus. Divide 20 by -2.

$$x=-10$$

Now solve the equation x=\frac{0±20}{-2} when ± is minus. Divide -20 by -2.

$$x=10$$

The equation is now solved.

$$x=-10 x=10$$