Solve 2x^2-20x+30

$$2 { x }^{ 2 } -20x+30$$

Factor

$$2\left(x-\left(5-\sqrt{10}\right)\right)\left(x-\left(\sqrt{10}+5\right)\right)$$

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.

$$2x^{2}-20x+30=0$$

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.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 2\times 30}}{2\times 2}$$

Square -20.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\times 2\times 30}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-20\right)±\sqrt{400-8\times 30}}{2\times 2}$$

Multiply -8 times 30.

$$x=\frac{-\left(-20\right)±\sqrt{400-240}}{2\times 2}$$

Add 400 to -240.

$$x=\frac{-\left(-20\right)±\sqrt{160}}{2\times 2}$$

Take the square root of 160.

$$x=\frac{-\left(-20\right)±4\sqrt{10}}{2\times 2}$$

The opposite of -20 is 20.

$$x=\frac{20±4\sqrt{10}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{20±4\sqrt{10}}{4}$$

Now solve the equation x=\frac{20±4\sqrt{10}}{4} when ± is plus. Add 20 to 4\sqrt{10}.

$$x=\frac{4\sqrt{10}+20}{4}$$

Divide 20+4\sqrt{10} by 4.

$$x=\sqrt{10}+5$$

Now solve the equation x=\frac{20±4\sqrt{10}}{4} when ± is minus. Subtract 4\sqrt{10} from 20.

$$x=\frac{20-4\sqrt{10}}{4}$$

Divide 20-4\sqrt{10} by 4.

$$x=5-\sqrt{10}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 5+\sqrt{10} for x_{1} and 5-\sqrt{10} for x_{2}.

$$2x^{2}-20x+30=2\left(x-\left(\sqrt{10}+5\right)\right)\left(x-\left(5-\sqrt{10}\right)\right)$$

Evaluate

$$2\left(x^{2}-10x+15\right)$$