Solve x^2+24x+12

$${ x }^{ 2 } +24x+12$$

Factor

$$\left(x-\left(-2\sqrt{33}-12\right)\right)\left(x-\left(2\sqrt{33}-12\right)\right)$$

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.

$$x^{2}+24x+12=0$$

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.

$$x=\frac{-24±\sqrt{24^{2}-4\times 12}}{2}$$

Square 24.

$$x=\frac{-24±\sqrt{576-4\times 12}}{2}$$

Multiply -4 times 12.

$$x=\frac{-24±\sqrt{576-48}}{2}$$

Add 576 to -48.

$$x=\frac{-24±\sqrt{528}}{2}$$

Take the square root of 528.

$$x=\frac{-24±4\sqrt{33}}{2}$$

Now solve the equation x=\frac{-24±4\sqrt{33}}{2} when ± is plus. Add -24 to 4\sqrt{33}.

$$x=\frac{4\sqrt{33}-24}{2}$$

Divide -24+4\sqrt{33} by 2.

$$x=2\sqrt{33}-12$$

Now solve the equation x=\frac{-24±4\sqrt{33}}{2} when ± is minus. Subtract 4\sqrt{33} from -24.

$$x=\frac{-4\sqrt{33}-24}{2}$$

Divide -24-4\sqrt{33} by 2.

$$x=-2\sqrt{33}-12$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -12+2\sqrt{33} for x_{1} and -12-2\sqrt{33} for x_{2}.

$$x^{2}+24x+12=\left(x-\left(2\sqrt{33}-12\right)\right)\left(x-\left(-2\sqrt{33}-12\right)\right)$$

Evaluate

$$x^{2}+24x+12$$