Solve 2x^2-20x+2

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

Factor

$$2\left(x-\left(5-2\sqrt{6}\right)\right)\left(x-\left(2\sqrt{6}+5\right)\right)$$

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.

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

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.

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

Square -20.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\times 2\times 2}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-20\right)±\sqrt{400-8\times 2}}{2\times 2}$$

Multiply -8 times 2.

$$x=\frac{-\left(-20\right)±\sqrt{400-16}}{2\times 2}$$

Add 400 to -16.

$$x=\frac{-\left(-20\right)±\sqrt{384}}{2\times 2}$$

Take the square root of 384.

$$x=\frac{-\left(-20\right)±8\sqrt{6}}{2\times 2}$$

The opposite of -20 is 20.

$$x=\frac{20±8\sqrt{6}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{20±8\sqrt{6}}{4}$$

Now solve the equation x=\frac{20±8\sqrt{6}}{4} when ± is plus. Add 20 to 8\sqrt{6}.

$$x=\frac{8\sqrt{6}+20}{4}$$

Divide 20+8\sqrt{6} by 4.

$$x=2\sqrt{6}+5$$

Now solve the equation x=\frac{20±8\sqrt{6}}{4} when ± is minus. Subtract 8\sqrt{6} from 20.

$$x=\frac{20-8\sqrt{6}}{4}$$

Divide 20-8\sqrt{6} by 4.

$$x=5-2\sqrt{6}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 5+2\sqrt{6} for x_{1} and 5-2\sqrt{6} for x_{2}.

$$2x^{2}-20x+2=2\left(x-\left(2\sqrt{6}+5\right)\right)\left(x-\left(5-2\sqrt{6}\right)\right)$$

Evaluate

$$2\left(x^{2}-10x+1\right)$$