Solve 4+2x=16/x+4+x

$$4 + 2 x = \frac { 16 } { x } + 4 + x$$

Solve for x

$$x=-4$$

$$x=4$$

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.

$$x\times 4+2xx=16+x\times 4+xx$$

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

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

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

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

Subtract x\times 4 from both sides.

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

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

$$2x^{2}=16+x^{2}$$

Subtract x^{2} from both sides.

$$2x^{2}-x^{2}=16$$

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

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

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.

$$x\times 4+2xx=16+x\times 4+xx$$

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

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

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

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

Subtract 16 from both sides.

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

Subtract x\times 4 from both sides.

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

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

$$2x^{2}-16=x^{2}$$

Subtract x^{2} from both sides.

$$2x^{2}-16-x^{2}=0$$

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

$$x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -16.

$$x=\frac{0±\sqrt{64}}{2}$$

Take the square root of 64.

$$x=\frac{0±8}{2}$$

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

$$x=4$$

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

$$x=-4$$

The equation is now solved.

$$x=4 x=-4$$