Solve left(2x+10right)left(2x+8right)=144

$$\left( 2x+10 \right) \left( 2x+8 \right) =144$$

Solve for x

$$x = \frac{\sqrt{145} - 9}{2} \approx 1.520797289$$

$$x=\frac{-\sqrt{145}-9}{2}\approx -10.520797289$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x+10 by 2x+8 and combine like terms.

$$4x^{2}+36x+80=144$$

Subtract 144 from both sides.

$$4x^{2}+36x+80-144=0$$

Subtract 144 from 80 to get -64.

$$4x^{2}+36x-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 36 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-36±\sqrt{36^{2}-4\times 4\left(-64\right)}}{2\times 4}$$

Square 36.

$$x=\frac{-36±\sqrt{1296-4\times 4\left(-64\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-36±\sqrt{1296-16\left(-64\right)}}{2\times 4}$$

Multiply -16 times -64.

$$x=\frac{-36±\sqrt{1296+1024}}{2\times 4}$$

Add 1296 to 1024.

$$x=\frac{-36±\sqrt{2320}}{2\times 4}$$

Take the square root of 2320.

$$x=\frac{-36±4\sqrt{145}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-36±4\sqrt{145}}{8}$$

Now solve the equation x=\frac{-36±4\sqrt{145}}{8} when ± is plus. Add -36 to 4\sqrt{145}.

$$x=\frac{4\sqrt{145}-36}{8}$$

Divide -36+4\sqrt{145} by 8.

$$x=\frac{\sqrt{145}-9}{2}$$

Now solve the equation x=\frac{-36±4\sqrt{145}}{8} when ± is minus. Subtract 4\sqrt{145} from -36.

$$x=\frac{-4\sqrt{145}-36}{8}$$

Divide -36-4\sqrt{145} by 8.

$$x=\frac{-\sqrt{145}-9}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{145}-9}{2} x=\frac{-\sqrt{145}-9}{2}$$

Steps for Completing the Square

Use the distributive property to multiply 2x+10 by 2x+8 and combine like terms.

$$4x^{2}+36x+80=144$$

Subtract 80 from both sides.

$$4x^{2}+36x=144-80$$

Subtract 80 from 144 to get 64.

$$4x^{2}+36x=64$$

Divide both sides by 4.

$$\frac{4x^{2}+36x}{4}=\frac{64}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\frac{36}{4}x=\frac{64}{4}$$

Divide 36 by 4.

$$x^{2}+9x=\frac{64}{4}$$

Divide 64 by 4.

$$x^{2}+9x=16$$

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.

$$x^{2}+9x+\left(\frac{9}{2}\right)^{2}=16+\left(\frac{9}{2}\right)^{2}$$

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

$$x^{2}+9x+\frac{81}{4}=16+\frac{81}{4}$$

Add 16 to \frac{81}{4}.

$$x^{2}+9x+\frac{81}{4}=\frac{145}{4}$$

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}.

$$\left(x+\frac{9}{2}\right)^{2}=\frac{145}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{9}{2}\right)^{2}}=\sqrt{\frac{145}{4}}$$

Simplify.

$$x+\frac{9}{2}=\frac{\sqrt{145}}{2} x+\frac{9}{2}=-\frac{\sqrt{145}}{2}$$

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

$$x=\frac{\sqrt{145}-9}{2} x=\frac{-\sqrt{145}-9}{2}$$