Solve 8x^2-2x-20x+10

$$8 x ^ { 2 } - 2 x - 20 x + 10$$

Factor

$$8\left(x-\frac{11-\sqrt{41}}{8}\right)\left(x-\frac{\sqrt{41}+11}{8}\right)$$

Steps Using the Quadratic Formula

Combine -2x and -20x to get -22x.

$$factor(8x^{2}-22x+10)$$

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.

$$8x^{2}-22x+10=0$$

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.

$$x=\frac{-\left(-22\right)±\sqrt{\left(-22\right)^{2}-4\times 8\times 10}}{2\times 8}$$

Square -22.

$$x=\frac{-\left(-22\right)±\sqrt{484-4\times 8\times 10}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{-\left(-22\right)±\sqrt{484-32\times 10}}{2\times 8}$$

Multiply -32 times 10.

$$x=\frac{-\left(-22\right)±\sqrt{484-320}}{2\times 8}$$

Add 484 to -320.

$$x=\frac{-\left(-22\right)±\sqrt{164}}{2\times 8}$$

Take the square root of 164.

$$x=\frac{-\left(-22\right)±2\sqrt{41}}{2\times 8}$$

The opposite of -22 is 22.

$$x=\frac{22±2\sqrt{41}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{22±2\sqrt{41}}{16}$$

Now solve the equation x=\frac{22±2\sqrt{41}}{16} when ± is plus. Add 22 to 2\sqrt{41}.

$$x=\frac{2\sqrt{41}+22}{16}$$

Divide 22+2\sqrt{41} by 16.

$$x=\frac{\sqrt{41}+11}{8}$$

Now solve the equation x=\frac{22±2\sqrt{41}}{16} when ± is minus. Subtract 2\sqrt{41} from 22.

$$x=\frac{22-2\sqrt{41}}{16}$$

Divide 22-2\sqrt{41} by 16.

$$x=\frac{11-\sqrt{41}}{8}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{11+\sqrt{41}}{8} for x_{1} and \frac{11-\sqrt{41}}{8} for x_{2}.

$$8x^{2}-22x+10=8\left(x-\frac{\sqrt{41}+11}{8}\right)\left(x-\frac{11-\sqrt{41}}{8}\right)$$

Evaluate

$$8x^{2}-22x+10$$

Solution Steps

Combine -2x and -20x to get -22x.

$$8x^{2}-22x+10$$