Solve (x-1.1)(x-0.85)+0.15*0.1=0

$$( x - 1.1 ) ( x - 0.85 ) + 0.15 \times 0.1 = 0$$

Solve for x

$$x=1$$

$$x=0.95$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-1.1 by x-0.85 and combine like terms.

$$x^{2}-1.95x+0.935+0.15\times 0.1=0$$

Multiply 0.15 and 0.1 to get 0.015.

$$x^{2}-1.95x+0.935+0.015=0$$

Add 0.935 and 0.015 to get 0.95.

$$x^{2}-1.95x+0.95=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -1.95 for b, and 0.95 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1.95\right)±\sqrt{\left(-1.95\right)^{2}-4\times 0.95}}{2}$$

Square -1.95 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\left(-1.95\right)±\sqrt{3.8025-4\times 0.95}}{2}$$

Multiply -4 times 0.95.

$$x=\frac{-\left(-1.95\right)±\sqrt{3.8025-3.8}}{2}$$

Add 3.8025 to -3.8 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-1.95\right)±\sqrt{0.0025}}{2}$$

Take the square root of 0.0025.

$$x=\frac{-\left(-1.95\right)±\frac{1}{20}}{2}$$

The opposite of -1.95 is 1.95.

$$x=\frac{1.95±\frac{1}{20}}{2}$$

Now solve the equation x=\frac{1.95±\frac{1}{20}}{2} when ± is plus. Add 1.95 to \frac{1}{20} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

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

Divide 2 by 2.

$$x=1$$

Now solve the equation x=\frac{1.95±\frac{1}{20}}{2} when ± is minus. Subtract \frac{1}{20} from 1.95 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{19}{10}}{2}$$

Divide \frac{19}{10} by 2.

$$x=\frac{19}{20}$$

The equation is now solved.

$$x=1 x=\frac{19}{20}$$

Steps for Completing the Square

Use the distributive property to multiply x-1.1 by x-0.85 and combine like terms.

$$x^{2}-1.95x+0.935+0.15\times 0.1=0$$

Multiply 0.15 and 0.1 to get 0.015.

$$x^{2}-1.95x+0.935+0.015=0$$

Add 0.935 and 0.015 to get 0.95.

$$x^{2}-1.95x+0.95=0$$

Subtract 0.95 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-1.95x=-0.95$$

Divide -1.95, the coefficient of the x term, by 2 to get -0.975. Then add the square of -0.975 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-1.95x+\left(-0.975\right)^{2}=-0.95+\left(-0.975\right)^{2}$$

Square -0.975 by squaring both the numerator and the denominator of the fraction.

$$x^{2}-1.95x+0.950625=-0.95+0.950625$$

Add -0.95 to 0.950625 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-1.95x+0.950625=0.000625$$

Factor x^{2}-1.95x+0.950625. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-0.975\right)^{2}=0.000625$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-0.975\right)^{2}}=\sqrt{0.000625}$$

Simplify.

$$x-0.975=\frac{1}{40} x-0.975=-\frac{1}{40}$$

Add 0.975 to both sides of the equation.

$$x=1 x=\frac{19}{20}$$