Solve (2x-1/5)(x-1)+2/5=0

$$( 2 x - \frac { 1 } { 5 } ) ( x - 1 ) + \frac { 2 } { 5 } = 0$$

Solve for x

$$x=\frac{3}{5}=0.6$$

$$x=\frac{1}{2}=0.5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x-\frac{1}{5} by x-1 and combine like terms.

$$2x^{2}-\frac{11}{5}x+\frac{1}{5}+\frac{2}{5}=0$$

Add \frac{1}{5} and \frac{2}{5} to get \frac{3}{5}.

$$2x^{2}-\frac{11}{5}x+\frac{3}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -\frac{11}{5} for b, and \frac{3}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{11}{5}\right)±\sqrt{\left(-\frac{11}{5}\right)^{2}-4\times 2\times \frac{3}{5}}}{2\times 2}$$

Square -\frac{11}{5} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\left(-\frac{11}{5}\right)±\sqrt{\frac{121}{25}-4\times 2\times \frac{3}{5}}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-\frac{11}{5}\right)±\sqrt{\frac{121}{25}-8\times \frac{3}{5}}}{2\times 2}$$

Multiply -8 times \frac{3}{5}.

$$x=\frac{-\left(-\frac{11}{5}\right)±\sqrt{\frac{121}{25}-\frac{24}{5}}}{2\times 2}$$

Add \frac{121}{25} to -\frac{24}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-\frac{11}{5}\right)±\sqrt{\frac{1}{25}}}{2\times 2}$$

Take the square root of \frac{1}{25}.

$$x=\frac{-\left(-\frac{11}{5}\right)±\frac{1}{5}}{2\times 2}$$

The opposite of -\frac{11}{5} is \frac{11}{5}.

$$x=\frac{\frac{11}{5}±\frac{1}{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{\frac{11}{5}±\frac{1}{5}}{4}$$

Now solve the equation x=\frac{\frac{11}{5}±\frac{1}{5}}{4} when ± is plus. Add \frac{11}{5} to \frac{1}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{12}{5}}{4}$$

Divide \frac{12}{5} by 4.

$$x=\frac{3}{5}$$

Now solve the equation x=\frac{\frac{11}{5}±\frac{1}{5}}{4} when ± is minus. Subtract \frac{1}{5} from \frac{11}{5} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$x=\frac{1}{2}$$

The equation is now solved.

$$x=\frac{3}{5} x=\frac{1}{2}$$

Steps for Completing the Square

Use the distributive property to multiply 2x-\frac{1}{5} by x-1 and combine like terms.

$$2x^{2}-\frac{11}{5}x+\frac{1}{5}+\frac{2}{5}=0$$

Add \frac{1}{5} and \frac{2}{5} to get \frac{3}{5}.

$$2x^{2}-\frac{11}{5}x+\frac{3}{5}=0$$

Subtract \frac{3}{5} from both sides. Anything subtracted from zero gives its negation.

$$2x^{2}-\frac{11}{5}x=-\frac{3}{5}$$

Divide both sides by 2.

$$\frac{2x^{2}-\frac{11}{5}x}{2}=-\frac{\frac{3}{5}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\left(-\frac{\frac{11}{5}}{2}\right)x=-\frac{\frac{3}{5}}{2}$$

Divide -\frac{11}{5} by 2.

$$x^{2}-\frac{11}{10}x=-\frac{\frac{3}{5}}{2}$$

Divide -\frac{3}{5} by 2.

$$x^{2}-\frac{11}{10}x=-\frac{3}{10}$$

Divide -\frac{11}{10}, the coefficient of the x term, by 2 to get -\frac{11}{20}. Then add the square of -\frac{11}{20} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{11}{10}x+\left(-\frac{11}{20}\right)^{2}=-\frac{3}{10}+\left(-\frac{11}{20}\right)^{2}$$

Square -\frac{11}{20} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{11}{10}x+\frac{121}{400}=-\frac{3}{10}+\frac{121}{400}$$

Add -\frac{3}{10} to \frac{121}{400} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{11}{10}x+\frac{121}{400}=\frac{1}{400}$$

Factor x^{2}-\frac{11}{10}x+\frac{121}{400}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{11}{20}\right)^{2}=\frac{1}{400}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{11}{20}\right)^{2}}=\sqrt{\frac{1}{400}}$$

Simplify.

$$x-\frac{11}{20}=\frac{1}{20} x-\frac{11}{20}=-\frac{1}{20}$$

Add \frac{11}{20} to both sides of the equation.

$$x=\frac{3}{5} x=\frac{1}{2}$$