Solve (x+6)(x+12)=27

$$(x+6)(x+12)=27$$

Solve for x

$$x=-15$$

$$x=-3$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+6 by x+12 and combine like terms.

$$x^{2}+18x+72=27$$

Subtract 27 from both sides.

$$x^{2}+18x+72-27=0$$

Subtract 27 from 72 to get 45.

$$x^{2}+18x+45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 18 for b, and 45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\times 45}}{2}$$

Square 18.

$$x=\frac{-18±\sqrt{324-4\times 45}}{2}$$

Multiply -4 times 45.

$$x=\frac{-18±\sqrt{324-180}}{2}$$

Add 324 to -180.

$$x=\frac{-18±\sqrt{144}}{2}$$

Take the square root of 144.

$$x=\frac{-18±12}{2}$$

Now solve the equation x=\frac{-18±12}{2} when ± is plus. Add -18 to 12.

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

Divide -6 by 2.

$$x=-3$$

Now solve the equation x=\frac{-18±12}{2} when ± is minus. Subtract 12 from -18.

$$x=-\frac{30}{2}$$

Divide -30 by 2.

$$x=-15$$

The equation is now solved.

$$x=-3 x=-15$$

Steps for Completing the Square

Use the distributive property to multiply x+6 by x+12 and combine like terms.

$$x^{2}+18x+72=27$$

Subtract 72 from both sides.

$$x^{2}+18x=27-72$$

Subtract 72 from 27 to get -45.

$$x^{2}+18x=-45$$

Divide 18, the coefficient of the x term, by 2 to get 9. Then add the square of 9 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+18x+9^{2}=-45+9^{2}$$

Square 9.

$$x^{2}+18x+81=-45+81$$

Add -45 to 81.

$$x^{2}+18x+81=36$$

Factor x^{2}+18x+81. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+9\right)^{2}=36$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{36}$$

Simplify.

$$x+9=6 x+9=-6$$

Subtract 9 from both sides of the equation.

$$x=-3 x=-15$$