Solve (2x+6)(2x+4)=120

$$( 2 x + 6 ) ( 2 x + 4 ) = 120$$

Solve for x

$$x=-8$$

$$x=3$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x+6 by 2x+4 and combine like terms.

$$4x^{2}+20x+24=120$$

Subtract 120 from both sides.

$$4x^{2}+20x+24-120=0$$

Subtract 120 from 24 to get -96.

$$4x^{2}+20x-96=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 20 for b, and -96 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}-4\times 4\left(-96\right)}}{2\times 4}$$

Square 20.

$$x=\frac{-20±\sqrt{400-4\times 4\left(-96\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-20±\sqrt{400-16\left(-96\right)}}{2\times 4}$$

Multiply -16 times -96.

$$x=\frac{-20±\sqrt{400+1536}}{2\times 4}$$

Add 400 to 1536.

$$x=\frac{-20±\sqrt{1936}}{2\times 4}$$

Take the square root of 1936.

$$x=\frac{-20±44}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-20±44}{8}$$

Now solve the equation x=\frac{-20±44}{8} when ± is plus. Add -20 to 44.

$$x=\frac{24}{8}$$

Divide 24 by 8.

$$x=3$$

Now solve the equation x=\frac{-20±44}{8} when ± is minus. Subtract 44 from -20.

$$x=-\frac{64}{8}$$

Divide -64 by 8.

$$x=-8$$

The equation is now solved.

$$x=3 x=-8$$

Steps for Completing the Square

Use the distributive property to multiply 2x+6 by 2x+4 and combine like terms.

$$4x^{2}+20x+24=120$$

Subtract 24 from both sides.

$$4x^{2}+20x=120-24$$

Subtract 24 from 120 to get 96.

$$4x^{2}+20x=96$$

Divide both sides by 4.

$$\frac{4x^{2}+20x}{4}=\frac{96}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\frac{20}{4}x=\frac{96}{4}$$

Divide 20 by 4.

$$x^{2}+5x=\frac{96}{4}$$

Divide 96 by 4.

$$x^{2}+5x=24$$

Divide 5, the coefficient of the x term, by 2 to get \frac{5}{2}. Then add the square of \frac{5}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=24+\left(\frac{5}{2}\right)^{2}$$

Square \frac{5}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+5x+\frac{25}{4}=24+\frac{25}{4}$$

Add 24 to \frac{25}{4}.

$$x^{2}+5x+\frac{25}{4}=\frac{121}{4}$$

Factor x^{2}+5x+\frac{25}{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}.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{121}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Simplify.

$$x+\frac{5}{2}=\frac{11}{2} x+\frac{5}{2}=-\frac{11}{2}$$

Subtract \frac{5}{2} from both sides of the equation.

$$x=3 x=-8$$