Solve (2x-2)(x+6)=36

$$(2x-2)(x+6)=36$$

Solve for x

$$x=-8$$

$$x=3$$

Steps Using the Quadratic Formula

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

$$2x^{2}+10x-12=36$$

Subtract 36 from both sides.

$$2x^{2}+10x-12-36=0$$

Subtract 36 from -12 to get -48.

$$2x^{2}+10x-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 10 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-10±\sqrt{10^{2}-4\times 2\left(-48\right)}}{2\times 2}$$

Square 10.

$$x=\frac{-10±\sqrt{100-4\times 2\left(-48\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-10±\sqrt{100-8\left(-48\right)}}{2\times 2}$$

Multiply -8 times -48.

$$x=\frac{-10±\sqrt{100+384}}{2\times 2}$$

Add 100 to 384.

$$x=\frac{-10±\sqrt{484}}{2\times 2}$$

Take the square root of 484.

$$x=\frac{-10±22}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-10±22}{4}$$

Now solve the equation x=\frac{-10±22}{4} when ± is plus. Add -10 to 22.

$$x=\frac{12}{4}$$

Divide 12 by 4.

$$x=3$$

Now solve the equation x=\frac{-10±22}{4} when ± is minus. Subtract 22 from -10.

$$x=-\frac{32}{4}$$

Divide -32 by 4.

$$x=-8$$

The equation is now solved.

$$x=3 x=-8$$

Steps for Completing the Square

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

$$2x^{2}+10x-12=36$$

Add 12 to both sides.

$$2x^{2}+10x=36+12$$

Add 36 and 12 to get 48.

$$2x^{2}+10x=48$$

Divide both sides by 2.

$$\frac{2x^{2}+10x}{2}=\frac{48}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\frac{10}{2}x=\frac{48}{2}$$

Divide 10 by 2.

$$x^{2}+5x=\frac{48}{2}$$

Divide 48 by 2.

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

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.

$$x=3 x=-8$$