Solve x^2-8x+2

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

Factor

$$\left(x-\left(4-\sqrt{14}\right)\right)\left(x-\left(\sqrt{14}+4\right)\right)$$

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.

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

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.

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

Square -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2}}{2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-8\right)±\sqrt{64-8}}{2}$$

Add 64 to -8.

$$x=\frac{-\left(-8\right)±\sqrt{56}}{2}$$

Take the square root of 56.

$$x=\frac{-\left(-8\right)±2\sqrt{14}}{2}$$

The opposite of -8 is 8.

$$x=\frac{8±2\sqrt{14}}{2}$$

Now solve the equation x=\frac{8±2\sqrt{14}}{2} when ± is plus. Add 8 to 2\sqrt{14}.

$$x=\frac{2\sqrt{14}+8}{2}$$

Divide 8+2\sqrt{14} by 2.

$$x=\sqrt{14}+4$$

Now solve the equation x=\frac{8±2\sqrt{14}}{2} when ± is minus. Subtract 2\sqrt{14} from 8.

$$x=\frac{8-2\sqrt{14}}{2}$$

Divide 8-2\sqrt{14} by 2.

$$x=4-\sqrt{14}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 4+\sqrt{14} for x_{1} and 4-\sqrt{14} for x_{2}.

$$x^{2}-8x+2=\left(x-\left(\sqrt{14}+4\right)\right)\left(x-\left(4-\sqrt{14}\right)\right)$$

Evaluate

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