Solve 20x^2-76x+4

$$20 { x }^{ 2 } -76x+4$$

Factor

$$20\left(x-\frac{19-\sqrt{341}}{10}\right)\left(x-\frac{\sqrt{341}+19}{10}\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$20x^{2}-76x+4=0$$

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.

$$x=\frac{-\left(-76\right)±\sqrt{\left(-76\right)^{2}-4\times 20\times 4}}{2\times 20}$$

Square -76.

$$x=\frac{-\left(-76\right)±\sqrt{5776-4\times 20\times 4}}{2\times 20}$$

Multiply -4 times 20.

$$x=\frac{-\left(-76\right)±\sqrt{5776-80\times 4}}{2\times 20}$$

Multiply -80 times 4.

$$x=\frac{-\left(-76\right)±\sqrt{5776-320}}{2\times 20}$$

Add 5776 to -320.

$$x=\frac{-\left(-76\right)±\sqrt{5456}}{2\times 20}$$

Take the square root of 5456.

$$x=\frac{-\left(-76\right)±4\sqrt{341}}{2\times 20}$$

The opposite of -76 is 76.

$$x=\frac{76±4\sqrt{341}}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{76±4\sqrt{341}}{40}$$

Now solve the equation x=\frac{76±4\sqrt{341}}{40} when ± is plus. Add 76 to 4\sqrt{341}.

$$x=\frac{4\sqrt{341}+76}{40}$$

Divide 76+4\sqrt{341} by 40.

$$x=\frac{\sqrt{341}+19}{10}$$

Now solve the equation x=\frac{76±4\sqrt{341}}{40} when ± is minus. Subtract 4\sqrt{341} from 76.

$$x=\frac{76-4\sqrt{341}}{40}$$

Divide 76-4\sqrt{341} by 40.

$$x=\frac{19-\sqrt{341}}{10}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{19+\sqrt{341}}{10} for x_{1} and \frac{19-\sqrt{341}}{10} for x_{2}.

$$20x^{2}-76x+4=20\left(x-\frac{\sqrt{341}+19}{10}\right)\left(x-\frac{19-\sqrt{341}}{10}\right)$$

Evaluate

$$20x^{2}-76x+4$$