Solve 8/x-(x-2)=2

$$\frac{ 8 }{ x } -(x-2)=2$$

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.

$$8-\left(x-2\right)x=2x$$

Use the distributive property to multiply -1 by x-2.

$$8+\left(-x+2\right)x=2x$$

Use the distributive property to multiply -x+2 by x.

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

Subtract 2x from both sides.

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

Combine 2x and -2x to get 0.

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

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by -1.

$$x^{2}=\frac{-8}{-1}$$

Fraction \frac{-8}{-1} can be simplified to 8 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=8$$

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.

$$8-\left(x-2\right)x=2x$$

Use the distributive property to multiply -1 by x-2.

$$8+\left(-x+2\right)x=2x$$

Use the distributive property to multiply -x+2 by x.

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

Subtract 2x from both sides.

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

Combine 2x and -2x to get 0.

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

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=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}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 8}}{2\left(-1\right)}$$

Multiply 4 times 8.

$$x=\frac{0±\sqrt{32}}{2\left(-1\right)}$$

Take the square root of 32.

$$x=\frac{0±4\sqrt{2}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±4\sqrt{2}}{-2}$$

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.

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