Solve 5/x=x/20

$$\frac { 5 } { x } = \frac { x } { 20 }$$

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 20x, the least common multiple of x,20.

$$20\times 5=xx$$

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

$$20\times 5=x^{2}$$

Multiply 20 and 5 to get 100.

$$100=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=100$$

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 20x, the least common multiple of x,20.

$$20\times 5=xx$$

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

$$20\times 5=x^{2}$$

Multiply 20 and 5 to get 100.

$$100=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=100$$

Subtract 100 from both sides.

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

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}.

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

Square 0.

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

Multiply -4 times -100.

$$x=\frac{0±\sqrt{400}}{2}$$

Take the square root of 400.

$$x=\frac{0±20}{2}$$

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.

$$x=10 x=-10$$