Solve (x+22)(3x+6)=1152

$$( x + 22 ) ( 3 x + 6 ) = 1152$$

Solve for x

$$x=-34$$

$$x=10$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+22 by 3x+6 and combine like terms.

$$3x^{2}+72x+132=1152$$

Subtract 1152 from both sides.

$$3x^{2}+72x+132-1152=0$$

Subtract 1152 from 132 to get -1020.

$$3x^{2}+72x-1020=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 72 for b, and -1020 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-72±\sqrt{72^{2}-4\times 3\left(-1020\right)}}{2\times 3}$$

Square 72.

$$x=\frac{-72±\sqrt{5184-4\times 3\left(-1020\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{-72±\sqrt{5184-12\left(-1020\right)}}{2\times 3}$$

Multiply -12 times -1020.

$$x=\frac{-72±\sqrt{5184+12240}}{2\times 3}$$

Add 5184 to 12240.

$$x=\frac{-72±\sqrt{17424}}{2\times 3}$$

Take the square root of 17424.

$$x=\frac{-72±132}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-72±132}{6}$$

Now solve the equation x=\frac{-72±132}{6} when ± is plus. Add -72 to 132.

$$x=\frac{60}{6}$$

Divide 60 by 6.

$$x=10$$

Now solve the equation x=\frac{-72±132}{6} when ± is minus. Subtract 132 from -72.

$$x=-\frac{204}{6}$$

Divide -204 by 6.

$$x=-34$$

The equation is now solved.

$$x=10 x=-34$$

Steps for Completing the Square

Use the distributive property to multiply x+22 by 3x+6 and combine like terms.

$$3x^{2}+72x+132=1152$$

Subtract 132 from both sides.

$$3x^{2}+72x=1152-132$$

Subtract 132 from 1152 to get 1020.

$$3x^{2}+72x=1020$$

Divide both sides by 3.

$$\frac{3x^{2}+72x}{3}=\frac{1020}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x^{2}+\frac{72}{3}x=\frac{1020}{3}$$

Divide 72 by 3.

$$x^{2}+24x=\frac{1020}{3}$$

Divide 1020 by 3.

$$x^{2}+24x=340$$

Divide 24, the coefficient of the x term, by 2 to get 12. Then add the square of 12 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+24x+12^{2}=340+12^{2}$$

Square 12.

$$x^{2}+24x+144=340+144$$

Add 340 to 144.

$$x^{2}+24x+144=484$$

Factor x^{2}+24x+144. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+12\right)^{2}=484$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+12\right)^{2}}=\sqrt{484}$$

Simplify.

$$x+12=22 x+12=-22$$

Subtract 12 from both sides of the equation.

$$x=10 x=-34$$