Solve 36=(2x+12)(x+1)

$$36=(2x+12)(x+1)$$

Solve for x

$$x = \frac{\sqrt{97} - 7}{2} \approx 1.424428901$$

$$x=\frac{-\sqrt{97}-7}{2}\approx -8.424428901$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x+12 by x+1 and combine like terms.

$$36=2x^{2}+14x+12$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}+14x+12=36$$

Subtract 36 from both sides.

$$2x^{2}+14x+12-36=0$$

Subtract 36 from 12 to get -24.

$$2x^{2}+14x-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 14 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14±\sqrt{14^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

Square 14.

$$x=\frac{-14±\sqrt{196-4\times 2\left(-24\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-14±\sqrt{196-8\left(-24\right)}}{2\times 2}$$

Multiply -8 times -24.

$$x=\frac{-14±\sqrt{196+192}}{2\times 2}$$

Add 196 to 192.

$$x=\frac{-14±\sqrt{388}}{2\times 2}$$

Take the square root of 388.

$$x=\frac{-14±2\sqrt{97}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-14±2\sqrt{97}}{4}$$

Now solve the equation x=\frac{-14±2\sqrt{97}}{4} when ± is plus. Add -14 to 2\sqrt{97}.

$$x=\frac{2\sqrt{97}-14}{4}$$

Divide -14+2\sqrt{97} by 4.

$$x=\frac{\sqrt{97}-7}{2}$$

Now solve the equation x=\frac{-14±2\sqrt{97}}{4} when ± is minus. Subtract 2\sqrt{97} from -14.

$$x=\frac{-2\sqrt{97}-14}{4}$$

Divide -14-2\sqrt{97} by 4.

$$x=\frac{-\sqrt{97}-7}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{97}-7}{2} x=\frac{-\sqrt{97}-7}{2}$$

Steps for Completing the Square

Use the distributive property to multiply 2x+12 by x+1 and combine like terms.

$$36=2x^{2}+14x+12$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}+14x+12=36$$

Subtract 12 from both sides.

$$2x^{2}+14x=36-12$$

Subtract 12 from 36 to get 24.

$$2x^{2}+14x=24$$

Divide both sides by 2.

$$\frac{2x^{2}+14x}{2}=\frac{24}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\frac{14}{2}x=\frac{24}{2}$$

Divide 14 by 2.

$$x^{2}+7x=\frac{24}{2}$$

Divide 24 by 2.

$$x^{2}+7x=12$$

Divide 7, the coefficient of the x term, by 2 to get \frac{7}{2}. Then add the square of \frac{7}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=12+\left(\frac{7}{2}\right)^{2}$$

Square \frac{7}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+7x+\frac{49}{4}=12+\frac{49}{4}$$

Add 12 to \frac{49}{4}.

$$x^{2}+7x+\frac{49}{4}=\frac{97}{4}$$

Factor x^{2}+7x+\frac{49}{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}.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{97}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{97}{4}}$$

Simplify.

$$x+\frac{7}{2}=\frac{\sqrt{97}}{2} x+\frac{7}{2}=-\frac{\sqrt{97}}{2}$$

Subtract \frac{7}{2} from both sides of the equation.

$$x=\frac{\sqrt{97}-7}{2} x=\frac{-\sqrt{97}-7}{2}$$