Solve (x+x+1.4)(x-0.5)/2=4.05

$$\frac { ( x + x + 1.4 ) ( x - 0.5 ) } { 2 } = 4.05$$

Solve for x

$$x=-2.2$$

$$x=2$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$\left(x+x+1.4\right)\left(x-0.5\right)=4.05\times 2$$

Combine x and x to get 2x.

$$\left(2x+1.4\right)\left(x-0.5\right)=4.05\times 2$$

Use the distributive property to multiply 2x+1.4 by x-0.5 and combine like terms.

$$2x^{2}+0.4x-0.7=4.05\times 2$$

Multiply 4.05 and 2 to get 8.1.

$$2x^{2}+0.4x-0.7=8.1$$

Subtract 8.1 from both sides.

$$2x^{2}+0.4x-0.7-8.1=0$$

Subtract 8.1 from -0.7 to get -8.8.

$$2x^{2}+0.4x-8.8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0.4 for b, and -8.8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.4±\sqrt{0.4^{2}-4\times 2\left(-8.8\right)}}{2\times 2}$$

Square 0.4 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-0.4±\sqrt{0.16-4\times 2\left(-8.8\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-0.4±\sqrt{0.16-8\left(-8.8\right)}}{2\times 2}$$

Multiply -8 times -8.8.

$$x=\frac{-0.4±\sqrt{0.16+70.4}}{2\times 2}$$

Add 0.16 to 70.4 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-0.4±\sqrt{70.56}}{2\times 2}$$

Take the square root of 70.56.

$$x=\frac{-0.4±\frac{42}{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-0.4±\frac{42}{5}}{4}$$

Now solve the equation x=\frac{-0.4±\frac{42}{5}}{4} when ± is plus. Add -0.4 to \frac{42}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{8}{4}$$

Divide 8 by 4.

$$x=2$$

Now solve the equation x=\frac{-0.4±\frac{42}{5}}{4} when ± is minus. Subtract \frac{42}{5} from -0.4 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{44}{5}}{4}$$

Divide -\frac{44}{5} by 4.

$$x=-\frac{11}{5}$$

The equation is now solved.

$$x=2 x=-\frac{11}{5}$$

Steps for Completing the Square

Multiply both sides by 2.

$$\left(x+x+1.4\right)\left(x-0.5\right)=4.05\times 2$$

Combine x and x to get 2x.

$$\left(2x+1.4\right)\left(x-0.5\right)=4.05\times 2$$

Use the distributive property to multiply 2x+1.4 by x-0.5 and combine like terms.

$$2x^{2}+0.4x-0.7=4.05\times 2$$

Multiply 4.05 and 2 to get 8.1.

$$2x^{2}+0.4x-0.7=8.1$$

Add 0.7 to both sides.

$$2x^{2}+0.4x=8.1+0.7$$

Add 8.1 and 0.7 to get 8.8.

$$2x^{2}+0.4x=8.8$$

Divide both sides by 2.

$$\frac{2x^{2}+0.4x}{2}=\frac{8.8}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\frac{0.4}{2}x=\frac{8.8}{2}$$

Divide 0.4 by 2.

$$x^{2}+0.2x=\frac{8.8}{2}$$

Divide 8.8 by 2.

$$x^{2}+0.2x=4.4$$

Divide 0.2, the coefficient of the x term, by 2 to get 0.1. Then add the square of 0.1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+0.2x+0.1^{2}=4.4+0.1^{2}$$

Square 0.1 by squaring both the numerator and the denominator of the fraction.

$$x^{2}+0.2x+0.01=4.4+0.01$$

Add 4.4 to 0.01 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+0.2x+0.01=4.41$$

Factor x^{2}+0.2x+0.01. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+0.1\right)^{2}=4.41$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+0.1\right)^{2}}=\sqrt{4.41}$$

Simplify.

$$x+0.1=\frac{21}{10} x+0.1=-\frac{21}{10}$$

Subtract 0.1 from both sides of the equation.

$$x=2 x=-\frac{11}{5}$$