Solve x^2+24x+10

$${ x }^{ 2 } +24x+10$$

Factor

$$\left(x-\left(-\sqrt{134}-12\right)\right)\left(x-\left(\sqrt{134}-12\right)\right)$$

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.

$$x^{2}+24x+10=0$$

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.

$$x=\frac{-24±\sqrt{24^{2}-4\times 10}}{2}$$

Square 24.

$$x=\frac{-24±\sqrt{576-4\times 10}}{2}$$

Multiply -4 times 10.

$$x=\frac{-24±\sqrt{576-40}}{2}$$

Add 576 to -40.

$$x=\frac{-24±\sqrt{536}}{2}$$

Take the square root of 536.

$$x=\frac{-24±2\sqrt{134}}{2}$$

Now solve the equation x=\frac{-24±2\sqrt{134}}{2} when ± is plus. Add -24 to 2\sqrt{134}.

$$x=\frac{2\sqrt{134}-24}{2}$$

Divide -24+2\sqrt{134} by 2.

$$x=\sqrt{134}-12$$

Now solve the equation x=\frac{-24±2\sqrt{134}}{2} when ± is minus. Subtract 2\sqrt{134} from -24.

$$x=\frac{-2\sqrt{134}-24}{2}$$

Divide -24-2\sqrt{134} by 2.

$$x=-\sqrt{134}-12$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -12+\sqrt{134} for x_{1} and -12-\sqrt{134} for x_{2}.

$$x^{2}+24x+10=\left(x-\left(\sqrt{134}-12\right)\right)\left(x-\left(-\sqrt{134}-12\right)\right)$$

Evaluate

$$x^{2}+24x+10$$