Solve (x+9)(x+6)=-2

$$(x+9)(x+6)=-2$$

Solve for x

$$x=-8$$

$$x=-7$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+9 by x+6 and combine like terms.

$$x^{2}+15x+54=-2$$

Add 2 to both sides.

$$x^{2}+15x+54+2=0$$

Add 54 and 2 to get 56.

$$x^{2}+15x+56=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 15 for b, and 56 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-15±\sqrt{15^{2}-4\times 56}}{2}$$

Square 15.

$$x=\frac{-15±\sqrt{225-4\times 56}}{2}$$

Multiply -4 times 56.

$$x=\frac{-15±\sqrt{225-224}}{2}$$

Add 225 to -224.

$$x=\frac{-15±\sqrt{1}}{2}$$

Take the square root of 1.

$$x=\frac{-15±1}{2}$$

Now solve the equation x=\frac{-15±1}{2} when ± is plus. Add -15 to 1.

$$x=-\frac{14}{2}$$

Divide -14 by 2.

$$x=-7$$

Now solve the equation x=\frac{-15±1}{2} when ± is minus. Subtract 1 from -15.

$$x=-\frac{16}{2}$$

Divide -16 by 2.

$$x=-8$$

The equation is now solved.

$$x=-7 x=-8$$

Steps for Completing the Square

Use the distributive property to multiply x+9 by x+6 and combine like terms.

$$x^{2}+15x+54=-2$$

Subtract 54 from both sides.

$$x^{2}+15x=-2-54$$

Subtract 54 from -2 to get -56.

$$x^{2}+15x=-56$$

Divide 15, the coefficient of the x term, by 2 to get \frac{15}{2}. Then add the square of \frac{15}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+15x+\left(\frac{15}{2}\right)^{2}=-56+\left(\frac{15}{2}\right)^{2}$$

Square \frac{15}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+15x+\frac{225}{4}=-56+\frac{225}{4}$$

Add -56 to \frac{225}{4}.

$$x^{2}+15x+\frac{225}{4}=\frac{1}{4}$$

Factor x^{2}+15x+\frac{225}{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}.

$$\left(x+\frac{15}{2}\right)^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{15}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Simplify.

$$x+\frac{15}{2}=\frac{1}{2} x+\frac{15}{2}=-\frac{1}{2}$$

Subtract \frac{15}{2} from both sides of the equation.

$$x=-7 x=-8$$