Solve left(-x-1right)left(x+10right)-12=0

$$\left( -x-1 \right) \left( x+10 \right) -12 = 0$$

Solve for x

$$x=\frac{\sqrt{33}-11}{2}\approx -2.627718677$$

$$x=\frac{-\sqrt{33}-11}{2}\approx -8.372281323$$

Steps Using the Quadratic Formula

Apply the distributive property by multiplying each term of -x-1 by each term of x+10.

$$\left(-x\right)x+10\left(-x\right)-x-10-12=0$$

Subtract 12 from -10 to get -22.

$$\left(-x\right)x+10\left(-x\right)-x-22=0$$

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

$$-x^{2}+10\left(-1\right)x-x-22=0$$

Multiply 10 and -1 to get -10.

$$-x^{2}-10x-x-22=0$$

Combine -10x and -x to get -11x.

$$-x^{2}-11x-22=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -11 for b, and -22 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\left(-1\right)\left(-22\right)}}{2\left(-1\right)}$$

Square -11.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\left(-1\right)\left(-22\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-11\right)±\sqrt{121+4\left(-22\right)}}{2\left(-1\right)}$$

Multiply 4 times -22.

$$x=\frac{-\left(-11\right)±\sqrt{121-88}}{2\left(-1\right)}$$

Add 121 to -88.

$$x=\frac{-\left(-11\right)±\sqrt{33}}{2\left(-1\right)}$$

The opposite of -11 is 11.

$$x=\frac{11±\sqrt{33}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{11±\sqrt{33}}{-2}$$

Now solve the equation x=\frac{11±\sqrt{33}}{-2} when ± is plus. Add 11 to \sqrt{33}.

$$x=\frac{\sqrt{33}+11}{-2}$$

Divide 11+\sqrt{33} by -2.

$$x=\frac{-\sqrt{33}-11}{2}$$

Now solve the equation x=\frac{11±\sqrt{33}}{-2} when ± is minus. Subtract \sqrt{33} from 11.

$$x=\frac{11-\sqrt{33}}{-2}$$

Divide 11-\sqrt{33} by -2.

$$x=\frac{\sqrt{33}-11}{2}$$

The equation is now solved.

$$x=\frac{-\sqrt{33}-11}{2} x=\frac{\sqrt{33}-11}{2}$$

Steps for Completing the Square

Apply the distributive property by multiplying each term of -x-1 by each term of x+10.

$$\left(-x\right)x+10\left(-x\right)-x-10-12=0$$

Subtract 12 from -10 to get -22.

$$\left(-x\right)x+10\left(-x\right)-x-22=0$$

Add 22 to both sides. Anything plus zero gives itself.

$$\left(-x\right)x+10\left(-x\right)-x=22$$

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

$$-x^{2}+10\left(-1\right)x-x=22$$

Multiply 10 and -1 to get -10.

$$-x^{2}-10x-x=22$$

Combine -10x and -x to get -11x.

$$-x^{2}-11x=22$$

Divide both sides by -1.

$$\frac{-x^{2}-11x}{-1}=\frac{22}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\left(-\frac{11}{-1}\right)x=\frac{22}{-1}$$

Divide -11 by -1.

$$x^{2}+11x=\frac{22}{-1}$$

Divide 22 by -1.

$$x^{2}+11x=-22$$

Divide 11, the coefficient of the x term, by 2 to get \frac{11}{2}. Then add the square of \frac{11}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+11x+\left(\frac{11}{2}\right)^{2}=-22+\left(\frac{11}{2}\right)^{2}$$

Square \frac{11}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+11x+\frac{121}{4}=-22+\frac{121}{4}$$

Add -22 to \frac{121}{4}.

$$x^{2}+11x+\frac{121}{4}=\frac{33}{4}$$

Factor x^{2}+11x+\frac{121}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{11}{2}\right)^{2}=\frac{33}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{11}{2}\right)^{2}}=\sqrt{\frac{33}{4}}$$

Simplify.

$$x+\frac{11}{2}=\frac{\sqrt{33}}{2} x+\frac{11}{2}=-\frac{\sqrt{33}}{2}$$

Subtract \frac{11}{2} from both sides of the equation.

$$x=\frac{\sqrt{33}-11}{2} x=\frac{-\sqrt{33}-11}{2}$$