Solve 385=(2x+2)*(2x+3)

$$385=(2x+2) \times (2x+3)$$

Solve for x

$$x = \frac{\sqrt{1541} - 5}{4} \approx 8.563893213$$

$$x=\frac{-\sqrt{1541}-5}{4}\approx -11.063893213$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x+2 by 2x+3 and combine like terms.

$$385=4x^{2}+10x+6$$

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

$$4x^{2}+10x+6=385$$

Subtract 385 from both sides.

$$4x^{2}+10x+6-385=0$$

Subtract 385 from 6 to get -379.

$$4x^{2}+10x-379=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 10 for b, and -379 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-10±\sqrt{10^{2}-4\times 4\left(-379\right)}}{2\times 4}$$

Square 10.

$$x=\frac{-10±\sqrt{100-4\times 4\left(-379\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-10±\sqrt{100-16\left(-379\right)}}{2\times 4}$$

Multiply -16 times -379.

$$x=\frac{-10±\sqrt{100+6064}}{2\times 4}$$

Add 100 to 6064.

$$x=\frac{-10±\sqrt{6164}}{2\times 4}$$

Take the square root of 6164.

$$x=\frac{-10±2\sqrt{1541}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-10±2\sqrt{1541}}{8}$$

Now solve the equation x=\frac{-10±2\sqrt{1541}}{8} when ± is plus. Add -10 to 2\sqrt{1541}.

$$x=\frac{2\sqrt{1541}-10}{8}$$

Divide -10+2\sqrt{1541} by 8.

$$x=\frac{\sqrt{1541}-5}{4}$$

Now solve the equation x=\frac{-10±2\sqrt{1541}}{8} when ± is minus. Subtract 2\sqrt{1541} from -10.

$$x=\frac{-2\sqrt{1541}-10}{8}$$

Divide -10-2\sqrt{1541} by 8.

$$x=\frac{-\sqrt{1541}-5}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{1541}-5}{4} x=\frac{-\sqrt{1541}-5}{4}$$

Steps for Completing the Square

Use the distributive property to multiply 2x+2 by 2x+3 and combine like terms.

$$385=4x^{2}+10x+6$$

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

$$4x^{2}+10x+6=385$$

Subtract 6 from both sides.

$$4x^{2}+10x=385-6$$

Subtract 6 from 385 to get 379.

$$4x^{2}+10x=379$$

Divide both sides by 4.

$$\frac{4x^{2}+10x}{4}=\frac{379}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\frac{10}{4}x=\frac{379}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{5}{2}x=\frac{379}{4}$$

Divide \frac{5}{2}, the coefficient of the x term, by 2 to get \frac{5}{4}. Then add the square of \frac{5}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{5}{2}x+\left(\frac{5}{4}\right)^{2}=\frac{379}{4}+\left(\frac{5}{4}\right)^{2}$$

Square \frac{5}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{379}{4}+\frac{25}{16}$$

Add \frac{379}{4} to \frac{25}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{1541}{16}$$

Factor x^{2}+\frac{5}{2}x+\frac{25}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{5}{4}\right)^{2}=\frac{1541}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{5}{4}\right)^{2}}=\sqrt{\frac{1541}{16}}$$

Simplify.

$$x+\frac{5}{4}=\frac{\sqrt{1541}}{4} x+\frac{5}{4}=-\frac{\sqrt{1541}}{4}$$

Subtract \frac{5}{4} from both sides of the equation.

$$x=\frac{\sqrt{1541}-5}{4} x=\frac{-\sqrt{1541}-5}{4}$$