Solve 16+x=-64/x

$$16 + x = - \frac { 64 } { x }$$

Solve for x

$$x=-8$$

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.

$$x\times 16+xx=-64$$

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

$$x\times 16+x^{2}=-64$$

Add 64 to both sides.

$$x\times 16+x^{2}+64=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x^{2}+16x+64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 16 for b, and 64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\times 64}}{2}$$

Square 16.

$$x=\frac{-16±\sqrt{256-4\times 64}}{2}$$

Multiply -4 times 64.

$$x=\frac{-16±\sqrt{256-256}}{2}$$

Add 256 to -256.

$$x=\frac{-16±\sqrt{0}}{2}$$

Take the square root of 0.

$$x=-\frac{16}{2}$$

Divide -16 by 2.

$$x=-8$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\times 16+xx=-64$$

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

$$x\times 16+x^{2}=-64$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}+16x=-64$$

Divide 16, the coefficient of the x term, by 2 to get 8. Then add the square of 8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+16x+8^{2}=-64+8^{2}$$

Square 8.

$$x^{2}+16x+64=-64+64$$

Add -64 to 64.

$$x^{2}+16x+64=0$$

Factor x^{2}+16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+8\right)^{2}=0$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{0}$$

Simplify.

$$x+8=0 x+8=0$$

Subtract 8 from both sides of the equation.

$$x=-8 x=-8$$

The equation is now solved. Solutions are the same.

$$x=-8$$