Solve 4+8x=4/x+4+4x

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

Solve for x

$$x=-1$$

$$x=1$$

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.

$$x\times 4+8xx=4+x\times 4+4xx$$

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

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

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

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

Subtract x\times 4 from both sides.

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

Combine x\times 4 and -x\times 4 to get 0.

$$8x^{2}=4+4x^{2}$$

Subtract 4x^{2} from both sides.

$$8x^{2}-4x^{2}=4$$

Combine 8x^{2} and -4x^{2} to get 4x^{2}.

$$4x^{2}=4$$

Divide both sides by 4.

$$x^{2}=\frac{4}{4}$$

Divide 4 by 4 to get 1.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

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.

$$x\times 4+8xx=4+x\times 4+4xx$$

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

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

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

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

Subtract 4 from both sides.

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

Subtract x\times 4 from both sides.

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

Combine x\times 4 and -x\times 4 to get 0.

$$8x^{2}-4=4x^{2}$$

Subtract 4x^{2} from both sides.

$$8x^{2}-4-4x^{2}=0$$

Combine 8x^{2} and -4x^{2} to get 4x^{2}.

$$4x^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-4\right)}}{2\times 4}$$

Multiply -16 times -4.

$$x=\frac{0±\sqrt{64}}{2\times 4}$$

Take the square root of 64.

$$x=\frac{0±8}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±8}{8}$$

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

$$x=1$$

Now solve the equation x=\frac{0±8}{8} when ± is minus. Divide -8 by 8.

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$