Solve (x+4)(x+5)=20

$$(x+4)(x+5)=20$$

Solve for x

$$x=-9$$

$$x=0$$

Steps Using the Quadratic Formula

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

$$x^{2}+9x+20=20$$

Subtract 20 from both sides.

$$x^{2}+9x+20-20=0$$

Subtract 20 from 20 to get 0.

$$x^{2}+9x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 9 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-9±\sqrt{9^{2}}}{2}$$

Take the square root of 9^{2}.

$$x=\frac{-9±9}{2}$$

Now solve the equation x=\frac{-9±9}{2} when ± is plus. Add -9 to 9.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-9±9}{2} when ± is minus. Subtract 9 from -9.

$$x=-\frac{18}{2}$$

Divide -18 by 2.

$$x=-9$$

The equation is now solved.

$$x=0 x=-9$$

Steps for Completing the Square

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

$$x^{2}+9x+20=20$$

Subtract 20 from both sides.

$$x^{2}+9x=20-20$$

Subtract 20 from 20 to get 0.

$$x^{2}+9x=0$$

Divide 9, the coefficient of the x term, by 2 to get \frac{9}{2}. Then add the square of \frac{9}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+9x+\left(\frac{9}{2}\right)^{2}=\left(\frac{9}{2}\right)^{2}$$

Square \frac{9}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+9x+\frac{81}{4}=\frac{81}{4}$$

Factor x^{2}+9x+\frac{81}{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}.

$$\left(x+\frac{9}{2}\right)^{2}=\frac{81}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{9}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Simplify.

$$x+\frac{9}{2}=\frac{9}{2} x+\frac{9}{2}=-\frac{9}{2}$$

Subtract \frac{9}{2} from both sides of the equation.

$$x=0 x=-9$$