Solve (x-5)(x+7)=-11

$$( x - 5 ) ( x + 7 ) = - 11$$

Solve for x

$$x=-6$$

$$x=4$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-5 by x+7 and combine like terms.

$$x^{2}+2x-35=-11$$

Add 11 to both sides.

$$x^{2}+2x-35+11=0$$

Add -35 and 11 to get -24.

$$x^{2}+2x-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-24\right)}}{2}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\left(-24\right)}}{2}$$

Multiply -4 times -24.

$$x=\frac{-2±\sqrt{4+96}}{2}$$

Add 4 to 96.

$$x=\frac{-2±\sqrt{100}}{2}$$

Take the square root of 100.

$$x=\frac{-2±10}{2}$$

Now solve the equation x=\frac{-2±10}{2} when ± is plus. Add -2 to 10.

$$x=\frac{8}{2}$$

Divide 8 by 2.

$$x=4$$

Now solve the equation x=\frac{-2±10}{2} when ± is minus. Subtract 10 from -2.

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

Divide -12 by 2.

$$x=-6$$

The equation is now solved.

$$x=4 x=-6$$

Steps for Completing the Square

Use the distributive property to multiply x-5 by x+7 and combine like terms.

$$x^{2}+2x-35=-11$$

Add 35 to both sides.

$$x^{2}+2x=-11+35$$

Add -11 and 35 to get 24.

$$x^{2}+2x=24$$

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+2x+1^{2}=24+1^{2}$$

Square 1.

$$x^{2}+2x+1=24+1$$

Add 24 to 1.

$$x^{2}+2x+1=25$$

Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+1\right)^{2}=25$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{25}$$

Simplify.

$$x+1=5 x+1=-5$$

Subtract 1 from both sides of the equation.

$$x=4 x=-6$$