Solve (1+x)(1+2x)=1.32

$$(1+x)(1+2x)=1.32$$

Solve for x

$$x=0.1$$

$$x=-1.6$$

Steps Using the Quadratic Formula

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

$$1+3x+2x^{2}=1.32$$

Subtract 1.32 from both sides.

$$1+3x+2x^{2}-1.32=0$$

Subtract 1.32 from 1 to get -0.32.

$$-0.32+3x+2x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$2x^{2}+3x-0.32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 3 for b, and -0.32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\times 2\left(-0.32\right)}}{2\times 2}$$

Square 3.

$$x=\frac{-3±\sqrt{9-4\times 2\left(-0.32\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-3±\sqrt{9-8\left(-0.32\right)}}{2\times 2}$$

Multiply -8 times -0.32.

$$x=\frac{-3±\sqrt{9+2.56}}{2\times 2}$$

Add 9 to 2.56.

$$x=\frac{-3±\sqrt{11.56}}{2\times 2}$$

Take the square root of 11.56.

$$x=\frac{-3±\frac{17}{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-3±\frac{17}{5}}{4}$$

Now solve the equation x=\frac{-3±\frac{17}{5}}{4} when ± is plus. Add -3 to \frac{17}{5}.

$$x=\frac{\frac{2}{5}}{4}$$

Divide \frac{2}{5} by 4.

$$x=\frac{1}{10}$$

Now solve the equation x=\frac{-3±\frac{17}{5}}{4} when ± is minus. Subtract \frac{17}{5} from -3.

$$x=-\frac{\frac{32}{5}}{4}$$

Divide -\frac{32}{5} by 4.

$$x=-\frac{8}{5}$$

The equation is now solved.

$$x=\frac{1}{10} x=-\frac{8}{5}$$

Steps for Completing the Square

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

$$1+3x+2x^{2}=1.32$$

Subtract 1 from both sides.

$$3x+2x^{2}=1.32-1$$

Subtract 1 from 1.32 to get 0.32.

$$3x+2x^{2}=0.32$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$2x^{2}+3x=0.32$$

Divide both sides by 2.

$$\frac{2x^{2}+3x}{2}=\frac{0.32}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\frac{3}{2}x=\frac{0.32}{2}$$

Divide 0.32 by 2.

$$x^{2}+\frac{3}{2}x=0.16$$

Divide \frac{3}{2}, the coefficient of the x term, by 2 to get \frac{3}{4}. Then add the square of \frac{3}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{3}{2}x+\left(\frac{3}{4}\right)^{2}=0.16+\left(\frac{3}{4}\right)^{2}$$

Square \frac{3}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=0.16+\frac{9}{16}$$

Add 0.16 to \frac{9}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=\frac{289}{400}$$

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

$$\left(x+\frac{3}{4}\right)^{2}=\frac{289}{400}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{3}{4}\right)^{2}}=\sqrt{\frac{289}{400}}$$

Simplify.

$$x+\frac{3}{4}=\frac{17}{20} x+\frac{3}{4}=-\frac{17}{20}$$

Subtract \frac{3}{4} from both sides of the equation.

$$x=\frac{1}{10} x=-\frac{8}{5}$$