Solve 9:x=x:64

$$9 : x = x : 64$$

Solve for x

$$x=24$$

$$x=-24$$

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 64x, the least common multiple of x,64.

$$64\times 9=xx$$

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

$$64\times 9=x^{2}$$

Multiply 64 and 9 to get 576.

$$576=x^{2}$$

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

$$x^{2}=576$$

Take the square root of both sides of the equation.

$$x=24 x=-24$$

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 64x, the least common multiple of x,64.

$$64\times 9=xx$$

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

$$64\times 9=x^{2}$$

Multiply 64 and 9 to get 576.

$$576=x^{2}$$

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

$$x^{2}=576$$

Subtract 576 from both sides.

$$x^{2}-576=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -576 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-576\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-576\right)}}{2}$$

Multiply -4 times -576.

$$x=\frac{0±\sqrt{2304}}{2}$$

Take the square root of 2304.

$$x=\frac{0±48}{2}$$

Now solve the equation x=\frac{0±48}{2} when ± is plus. Divide 48 by 2.

$$x=24$$

Now solve the equation x=\frac{0±48}{2} when ± is minus. Divide -48 by 2.

$$x=-24$$

The equation is now solved.

$$x=24 x=-24$$