Solve x+2-8/x=2

$$x + 2 - \frac { 8 } { x } = 2$$

Solve for x

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=-2\sqrt{2}\approx -2.828427125$$

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 x.

$$xx+x\times 2-8=2x$$

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

$$x^{2}+x\times 2-8=2x$$

Subtract 2x from both sides.

$$x^{2}+x\times 2-8-2x=0$$

Combine x\times 2 and -2x to get 0.

$$x^{2}-8=0$$

Add 8 to both sides. Anything plus zero gives itself.

$$x^{2}=8$$

Take the square root of both sides of the equation.

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

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 x.

$$xx+x\times 2-8=2x$$

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

$$x^{2}+x\times 2-8=2x$$

Subtract 2x from both sides.

$$x^{2}+x\times 2-8-2x=0$$

Combine x\times 2 and -2x to get 0.

$$x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-8\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-8\right)}}{2}$$

Multiply -4 times -8.

$$x=\frac{0±\sqrt{32}}{2}$$

Take the square root of 32.

$$x=\frac{0±4\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{2}}{2} when ± is plus.

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

Now solve the equation x=\frac{0±4\sqrt{2}}{2} when ± is minus.

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

The equation is now solved.

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