Solve [2(x+1)-1](x+1)=1.1232

$$[ 2 ( x + 1 ) - 1 ] ( x + 1 ) = 1.1232$$

Solve for x

$$x=0.04$$

$$x=-1.54$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2 by x+1.

$$\left(2x+2-1\right)\left(x+1\right)=1.1232$$

Subtract 1 from 2 to get 1.

$$\left(2x+1\right)\left(x+1\right)=1.1232$$

Apply the distributive property by multiplying each term of 2x+1 by each term of x+1.

$$2x^{2}+2x+x+1=1.1232$$

Combine 2x and x to get 3x.

$$2x^{2}+3x+1=1.1232$$

Subtract 1.1232 from both sides.

$$2x^{2}+3x+1-1.1232=0$$

Subtract 1.1232 from 1 to get -0.1232.

$$2x^{2}+3x-0.1232=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 3 for b, and -0.1232 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\times 2\left(-0.1232\right)}}{2\times 2}$$

Square 3.

$$x=\frac{-3±\sqrt{9-4\times 2\left(-0.1232\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-3±\sqrt{9-8\left(-0.1232\right)}}{2\times 2}$$

Multiply -8 times -0.1232.

$$x=\frac{-3±\sqrt{9+0.9856}}{2\times 2}$$

Add 9 to 0.9856.

$$x=\frac{-3±\sqrt{9.9856}}{2\times 2}$$

Take the square root of 9.9856.

$$x=\frac{-3±\frac{79}{25}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-3±\frac{79}{25}}{4}$$

Now solve the equation x=\frac{-3±\frac{79}{25}}{4} when ± is plus. Add -3 to \frac{79}{25}.

$$x=\frac{\frac{4}{25}}{4}$$

Divide \frac{4}{25} by 4.

$$x=\frac{1}{25}$$

Now solve the equation x=\frac{-3±\frac{79}{25}}{4} when ± is minus. Subtract \frac{79}{25} from -3.

$$x=-\frac{\frac{154}{25}}{4}$$

Divide -\frac{154}{25} by 4.

$$x=-\frac{77}{50}$$

The equation is now solved.

$$x=\frac{1}{25} x=-\frac{77}{50}$$

Steps for Completing the Square

Use the distributive property to multiply 2 by x+1.

$$\left(2x+2-1\right)\left(x+1\right)=1.1232$$

Subtract 1 from 2 to get 1.

$$\left(2x+1\right)\left(x+1\right)=1.1232$$

Apply the distributive property by multiplying each term of 2x+1 by each term of x+1.

$$2x^{2}+2x+x+1=1.1232$$

Combine 2x and x to get 3x.

$$2x^{2}+3x+1=1.1232$$

Subtract 1 from both sides.

$$2x^{2}+3x=1.1232-1$$

Subtract 1 from 1.1232 to get 0.1232.

$$2x^{2}+3x=0.1232$$

Divide both sides by 2.

$$\frac{2x^{2}+3x}{2}=\frac{0.1232}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\frac{3}{2}x=\frac{0.1232}{2}$$

Divide 0.1232 by 2.

$$x^{2}+\frac{3}{2}x=0.0616$$

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.

$$x^{2}+\frac{3}{2}x+\left(\frac{3}{4}\right)^{2}=0.0616+\left(\frac{3}{4}\right)^{2}$$

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

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=0.0616+\frac{9}{16}$$

Add 0.0616 to \frac{9}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=\frac{6241}{10000}$$

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}.

$$\left(x+\frac{3}{4}\right)^{2}=\frac{6241}{10000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{3}{4}\right)^{2}}=\sqrt{\frac{6241}{10000}}$$

Simplify.

$$x+\frac{3}{4}=\frac{79}{100} x+\frac{3}{4}=-\frac{79}{100}$$

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

$$x=\frac{1}{25} x=-\frac{77}{50}$$