Solve 8/x=x/18

$$\frac{ 8 }{ x } = \frac{ x }{ 18 }$$

Solve for x

$$x=12$$

$$x=-12$$

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 18x, the least common multiple of x,18.

$$18\times 8=xx$$

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

$$18\times 8=x^{2}$$

Multiply 18 and 8 to get 144.

$$144=x^{2}$$

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

$$x^{2}=144$$

Take the square root of both sides of the equation.

$$x=12 x=-12$$

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 18x, the least common multiple of x,18.

$$18\times 8=xx$$

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

$$18\times 8=x^{2}$$

Multiply 18 and 8 to get 144.

$$144=x^{2}$$

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

$$x^{2}=144$$

Subtract 144 from both sides.

$$x^{2}-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-144\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-144\right)}}{2}$$

Multiply -4 times -144.

$$x=\frac{0±\sqrt{576}}{2}$$

Take the square root of 576.

$$x=\frac{0±24}{2}$$

Now solve the equation x=\frac{0±24}{2} when ± is plus. Divide 24 by 2.

$$x=12$$

Now solve the equation x=\frac{0±24}{2} when ± is minus. Divide -24 by 2.

$$x=-12$$

The equation is now solved.

$$x=12 x=-12$$