Solve x^2-18x+12

$${ x }^{ 2 } -18x+12$$

Factor

$$\left(x-\left(9-\sqrt{69}\right)\right)\left(x-\left(\sqrt{69}+9\right)\right)$$

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.

$$x^{2}-18x+12=0$$

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.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 12}}{2}$$

Square -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 12}}{2}$$

Multiply -4 times 12.

$$x=\frac{-\left(-18\right)±\sqrt{324-48}}{2}$$

Add 324 to -48.

$$x=\frac{-\left(-18\right)±\sqrt{276}}{2}$$

Take the square root of 276.

$$x=\frac{-\left(-18\right)±2\sqrt{69}}{2}$$

The opposite of -18 is 18.

$$x=\frac{18±2\sqrt{69}}{2}$$

Now solve the equation x=\frac{18±2\sqrt{69}}{2} when ± is plus. Add 18 to 2\sqrt{69}.

$$x=\frac{2\sqrt{69}+18}{2}$$

Divide 18+2\sqrt{69} by 2.

$$x=\sqrt{69}+9$$

Now solve the equation x=\frac{18±2\sqrt{69}}{2} when ± is minus. Subtract 2\sqrt{69} from 18.

$$x=\frac{18-2\sqrt{69}}{2}$$

Divide 18-2\sqrt{69} by 2.

$$x=9-\sqrt{69}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 9+\sqrt{69} for x_{1} and 9-\sqrt{69} for x_{2}.

$$x^{2}-18x+12=\left(x-\left(\sqrt{69}+9\right)\right)\left(x-\left(9-\sqrt{69}\right)\right)$$

Evaluate

$$x^{2}-18x+12$$