Solve (x-4)(x+5)=-8

$$( x - 4 ) ( x + 5 ) = - 8$$

Solve for x

$$x=-4$$

$$x=3$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-4 by x+5 and combine like terms.

$$x^{2}+x-20=-8$$

Add 8 to both sides.

$$x^{2}+x-20+8=0$$

Add -20 and 8 to get -12.

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

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

$$x=\frac{-1±\sqrt{1^{2}-4\left(-12\right)}}{2}$$

Square 1.

$$x=\frac{-1±\sqrt{1-4\left(-12\right)}}{2}$$

Multiply -4 times -12.

$$x=\frac{-1±\sqrt{1+48}}{2}$$

Add 1 to 48.

$$x=\frac{-1±\sqrt{49}}{2}$$

Take the square root of 49.

$$x=\frac{-1±7}{2}$$

Now solve the equation x=\frac{-1±7}{2} when ± is plus. Add -1 to 7.

$$x=\frac{6}{2}$$

Divide 6 by 2.

$$x=3$$

Now solve the equation x=\frac{-1±7}{2} when ± is minus. Subtract 7 from -1.

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

Divide -8 by 2.

$$x=-4$$

The equation is now solved.

$$x=3 x=-4$$

Steps for Completing the Square

Use the distributive property to multiply x-4 by x+5 and combine like terms.

$$x^{2}+x-20=-8$$

Add 20 to both sides.

$$x^{2}+x=-8+20$$

Add -8 and 20 to get 12.

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

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

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=12+\left(\frac{1}{2}\right)^{2}$$

Square \frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+x+\frac{1}{4}=12+\frac{1}{4}$$

Add 12 to \frac{1}{4}.

$$x^{2}+x+\frac{1}{4}=\frac{49}{4}$$

Factor x^{2}+x+\frac{1}{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}.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Simplify.

$$x+\frac{1}{2}=\frac{7}{2} x+\frac{1}{2}=-\frac{7}{2}$$

Subtract \frac{1}{2} from both sides of the equation.

$$x=3 x=-4$$