Solve -2x+12=-80/x

$$- 2 x + 12 = - \frac { 80 } { x }$$

Solve for x

$$x=-4$$

$$x=10$$

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.

$$-2xx+x\times 12=-80$$

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

$$-2x^{2}+x\times 12=-80$$

Add 80 to both sides.

$$-2x^{2}+x\times 12+80=0$$

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.

$$-2x^{2}+12x+80=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 12 for b, and 80 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-2\right)\times 80}}{2\left(-2\right)}$$

Square 12.

$$x=\frac{-12±\sqrt{144-4\left(-2\right)\times 80}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{-12±\sqrt{144+8\times 80}}{2\left(-2\right)}$$

Multiply 8 times 80.

$$x=\frac{-12±\sqrt{144+640}}{2\left(-2\right)}$$

Add 144 to 640.

$$x=\frac{-12±\sqrt{784}}{2\left(-2\right)}$$

Take the square root of 784.

$$x=\frac{-12±28}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{-12±28}{-4}$$

Now solve the equation x=\frac{-12±28}{-4} when ± is plus. Add -12 to 28.

$$x=\frac{16}{-4}$$

Divide 16 by -4.

$$x=-4$$

Now solve the equation x=\frac{-12±28}{-4} when ± is minus. Subtract 28 from -12.

$$x=-\frac{40}{-4}$$

Divide -40 by -4.

$$x=10$$

The equation is now solved.

$$x=-4 x=10$$

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.

$$-2xx+x\times 12=-80$$

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

$$-2x^{2}+x\times 12=-80$$

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.

$$-2x^{2}+12x=-80$$

Divide both sides by -2.

$$\frac{-2x^{2}+12x}{-2}=-\frac{80}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x^{2}+\frac{12}{-2}x=-\frac{80}{-2}$$

Divide 12 by -2.

$$x^{2}-6x=-\frac{80}{-2}$$

Divide -80 by -2.

$$x^{2}-6x=40$$

Divide -6, the coefficient of the x term, by 2 to get -3. Then add the square of -3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-6x+\left(-3\right)^{2}=40+\left(-3\right)^{2}$$

Square -3.

$$x^{2}-6x+9=40+9$$

Add 40 to 9.

$$x^{2}-6x+9=49$$

Factor x^{2}-6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-3\right)^{2}=49$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{49}$$

Simplify.

$$x-3=7 x-3=-7$$

Add 3 to both sides of the equation.

$$x=10 x=-4$$