Solve x*(x+12)=85

$$x \times (x+12)=85$$

Solve for x

$$x=-17$$

$$x=5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x+12.

$$x^{2}+12x=85$$

Subtract 85 from both sides.

$$x^{2}+12x-85=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 12 for b, and -85 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-85\right)}}{2}$$

Square 12.

$$x=\frac{-12±\sqrt{144-4\left(-85\right)}}{2}$$

Multiply -4 times -85.

$$x=\frac{-12±\sqrt{144+340}}{2}$$

Add 144 to 340.

$$x=\frac{-12±\sqrt{484}}{2}$$

Take the square root of 484.

$$x=\frac{-12±22}{2}$$

Now solve the equation x=\frac{-12±22}{2} when ± is plus. Add -12 to 22.

$$x=\frac{10}{2}$$

Divide 10 by 2.

$$x=5$$

Now solve the equation x=\frac{-12±22}{2} when ± is minus. Subtract 22 from -12.

$$x=-\frac{34}{2}$$

Divide -34 by 2.

$$x=-17$$

The equation is now solved.

$$x=5 x=-17$$

Steps for Completing the Square

Use the distributive property to multiply x by x+12.

$$x^{2}+12x=85$$

Divide 12, the coefficient of the x term, by 2 to get 6. Then add the square of 6 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+12x+6^{2}=85+6^{2}$$

Square 6.

$$x^{2}+12x+36=85+36$$

Add 85 to 36.

$$x^{2}+12x+36=121$$

Factor x^{2}+12x+36. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+6\right)^{2}=121$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{121}$$

Simplify.

$$x+6=11 x+6=-11$$

Subtract 6 from both sides of the equation.

$$x=5 x=-17$$