Solve 4x(2x+2)=240

$$4 x ( 2 x + 2 ) = 240$$

Solve for x

$$x=-6$$

$$x=5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 4x by 2x+2.

$$8x^{2}+8x=240$$

Subtract 240 from both sides.

$$8x^{2}+8x-240=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 8 for b, and -240 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times 8\left(-240\right)}}{2\times 8}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\times 8\left(-240\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{-8±\sqrt{64-32\left(-240\right)}}{2\times 8}$$

Multiply -32 times -240.

$$x=\frac{-8±\sqrt{64+7680}}{2\times 8}$$

Add 64 to 7680.

$$x=\frac{-8±\sqrt{7744}}{2\times 8}$$

Take the square root of 7744.

$$x=\frac{-8±88}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-8±88}{16}$$

Now solve the equation x=\frac{-8±88}{16} when ± is plus. Add -8 to 88.

$$x=\frac{80}{16}$$

Divide 80 by 16.

$$x=5$$

Now solve the equation x=\frac{-8±88}{16} when ± is minus. Subtract 88 from -8.

$$x=-\frac{96}{16}$$

Divide -96 by 16.

$$x=-6$$

The equation is now solved.

$$x=5 x=-6$$

Steps for Completing the Square

Use the distributive property to multiply 4x by 2x+2.

$$8x^{2}+8x=240$$

Divide both sides by 8.

$$\frac{8x^{2}+8x}{8}=\frac{240}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x^{2}+\frac{8}{8}x=\frac{240}{8}$$

Divide 8 by 8.

$$x^{2}+x=\frac{240}{8}$$

Divide 240 by 8.

$$x^{2}+x=30$$

Divide 1, the coefficient of the x term, by 2 to get \frac{1}{2}. Then add the square of \frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=30+\left(\frac{1}{2}\right)^{2}$$

Square \frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+x+\frac{1}{4}=30+\frac{1}{4}$$

Add 30 to \frac{1}{4}.

$$x^{2}+x+\frac{1}{4}=\frac{121}{4}$$

Factor x^{2}+x+\frac{1}{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}.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{121}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Simplify.

$$x+\frac{1}{2}=\frac{11}{2} x+\frac{1}{2}=-\frac{11}{2}$$

Subtract \frac{1}{2} from both sides of the equation.

$$x=5 x=-6$$