Solve 3/x=x/12

$$\frac { 3 } { x } = \frac { x } { 12 }$$

Solve for x

$$x=6$$

$$x=-6$$

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 12x, the least common multiple of x,12.

$$12\times 3=xx$$

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

$$12\times 3=x^{2}$$

Multiply 12 and 3 to get 36.

$$36=x^{2}$$

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

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

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 12x, the least common multiple of x,12.

$$12\times 3=xx$$

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

$$12\times 3=x^{2}$$

Multiply 12 and 3 to get 36.

$$36=x^{2}$$

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

$$x^{2}=36$$

Subtract 36 from both sides.

$$x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$

Multiply -4 times -36.

$$x=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$x=\frac{0±12}{2}$$

Now solve the equation x=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$x=6$$

Now solve the equation x=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$