Solve left(x+1right)3(x+2)=1064

$$\left( x+1 \right) 3(x+2) = 1064$$

Solve for x

$$x=\frac{\sqrt{12777}}{6}-\frac{3}{2}\approx 17.339232115$$

$$x=-\frac{\sqrt{12777}}{6}-\frac{3}{2}\approx -20.339232115$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+1 by 3.

$$\left(3x+3\right)\left(x+2\right)=1064$$

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

$$3x^{2}+9x+6=1064$$

Subtract 1064 from both sides.

$$3x^{2}+9x+6-1064=0$$

Subtract 1064 from 6 to get -1058.

$$3x^{2}+9x-1058=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 9 for b, and -1058 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-9±\sqrt{9^{2}-4\times 3\left(-1058\right)}}{2\times 3}$$

Square 9.

$$x=\frac{-9±\sqrt{81-4\times 3\left(-1058\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{-9±\sqrt{81-12\left(-1058\right)}}{2\times 3}$$

Multiply -12 times -1058.

$$x=\frac{-9±\sqrt{81+12696}}{2\times 3}$$

Add 81 to 12696.

$$x=\frac{-9±\sqrt{12777}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-9±\sqrt{12777}}{6}$$

Now solve the equation x=\frac{-9±\sqrt{12777}}{6} when ± is plus. Add -9 to \sqrt{12777}.

$$x=\frac{\sqrt{12777}-9}{6}$$

Divide -9+\sqrt{12777} by 6.

$$x=\frac{\sqrt{12777}}{6}-\frac{3}{2}$$

Now solve the equation x=\frac{-9±\sqrt{12777}}{6} when ± is minus. Subtract \sqrt{12777} from -9.

$$x=\frac{-\sqrt{12777}-9}{6}$$

Divide -9-\sqrt{12777} by 6.

$$x=-\frac{\sqrt{12777}}{6}-\frac{3}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{12777}}{6}-\frac{3}{2} x=-\frac{\sqrt{12777}}{6}-\frac{3}{2}$$

Steps for Completing the Square

Use the distributive property to multiply x+1 by 3.

$$\left(3x+3\right)\left(x+2\right)=1064$$

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

$$3x^{2}+9x+6=1064$$

Subtract 6 from both sides.

$$3x^{2}+9x=1064-6$$

Subtract 6 from 1064 to get 1058.

$$3x^{2}+9x=1058$$

Divide both sides by 3.

$$\frac{3x^{2}+9x}{3}=\frac{1058}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x^{2}+\frac{9}{3}x=\frac{1058}{3}$$

Divide 9 by 3.

$$x^{2}+3x=\frac{1058}{3}$$

Divide 3, the coefficient of the x term, by 2 to get \frac{3}{2}. Then add the square of \frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=\frac{1058}{3}+\left(\frac{3}{2}\right)^{2}$$

Square \frac{3}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+3x+\frac{9}{4}=\frac{1058}{3}+\frac{9}{4}$$

Add \frac{1058}{3} to \frac{9}{4} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+3x+\frac{9}{4}=\frac{4259}{12}$$

Factor x^{2}+3x+\frac{9}{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}.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{4259}{12}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{4259}{12}}$$

Simplify.

$$x+\frac{3}{2}=\frac{\sqrt{12777}}{6} x+\frac{3}{2}=-\frac{\sqrt{12777}}{6}$$

Subtract \frac{3}{2} from both sides of the equation.

$$x=\frac{\sqrt{12777}}{6}-\frac{3}{2} x=-\frac{\sqrt{12777}}{6}-\frac{3}{2}$$