Solve x/16=4/x

$$\frac { x } { 16 } = \frac { 4 } { x }$$

Solve for x

$$x=8$$

$$x=-8$$

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 16x, the least common multiple of 16,x.

$$xx=16\times 4$$

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

$$x^{2}=16\times 4$$

Multiply 16 and 4 to get 64.

$$x^{2}=64$$

Take the square root of both sides of the equation.

$$x=8 x=-8$$

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 16x, the least common multiple of 16,x.

$$xx=16\times 4$$

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

$$x^{2}=16\times 4$$

Multiply 16 and 4 to get 64.

$$x^{2}=64$$

Subtract 64 from both sides.

$$x^{2}-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-64\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-64\right)}}{2}$$

Multiply -4 times -64.

$$x=\frac{0±\sqrt{256}}{2}$$

Take the square root of 256.

$$x=\frac{0±16}{2}$$

Now solve the equation x=\frac{0±16}{2} when ± is plus. Divide 16 by 2.

$$x=8$$

Now solve the equation x=\frac{0±16}{2} when ± is minus. Divide -16 by 2.

$$x=-8$$

The equation is now solved.

$$x=8 x=-8$$