Solve x/4=8/x

$$\frac { x } { 4 } = \frac { 8 } { x }$$

Solve for x

$$x=4\sqrt{2}\approx 5.656854249$$

$$x=-4\sqrt{2}\approx -5.656854249$$

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 4x, the least common multiple of 4,x.

$$xx=4\times 8$$

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

$$x^{2}=4\times 8$$

Multiply 4 and 8 to get 32.

$$x^{2}=32$$

Take the square root of both sides of the equation.

$$x=4\sqrt{2} x=-4\sqrt{2}$$

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 4x, the least common multiple of 4,x.

$$xx=4\times 8$$

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

$$x^{2}=4\times 8$$

Multiply 4 and 8 to get 32.

$$x^{2}=32$$

Subtract 32 from both sides.

$$x^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-32\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-32\right)}}{2}$$

Multiply -4 times -32.

$$x=\frac{0±\sqrt{128}}{2}$$

Take the square root of 128.

$$x=\frac{0±8\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{2}}{2} when ± is plus.

$$x=4\sqrt{2}$$

Now solve the equation x=\frac{0±8\sqrt{2}}{2} when ± is minus.

$$x=-4\sqrt{2}$$

The equation is now solved.

$$x=4\sqrt{2} x=-4\sqrt{2}$$