Solve x^2+34x-24

$${ x }^{ 2 } +34x-24$$

Factor

$$\left(x-\left(-\sqrt{313}-17\right)\right)\left(x-\left(\sqrt{313}-17\right)\right)$$

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.

$$x^{2}+34x-24=0$$

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.

$$x=\frac{-34±\sqrt{34^{2}-4\left(-24\right)}}{2}$$

Square 34.

$$x=\frac{-34±\sqrt{1156-4\left(-24\right)}}{2}$$

Multiply -4 times -24.

$$x=\frac{-34±\sqrt{1156+96}}{2}$$

Add 1156 to 96.

$$x=\frac{-34±\sqrt{1252}}{2}$$

Take the square root of 1252.

$$x=\frac{-34±2\sqrt{313}}{2}$$

Now solve the equation x=\frac{-34±2\sqrt{313}}{2} when ± is plus. Add -34 to 2\sqrt{313}.

$$x=\frac{2\sqrt{313}-34}{2}$$

Divide -34+2\sqrt{313} by 2.

$$x=\sqrt{313}-17$$

Now solve the equation x=\frac{-34±2\sqrt{313}}{2} when ± is minus. Subtract 2\sqrt{313} from -34.

$$x=\frac{-2\sqrt{313}-34}{2}$$

Divide -34-2\sqrt{313} by 2.

$$x=-\sqrt{313}-17$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -17+\sqrt{313} for x_{1} and -17-\sqrt{313} for x_{2}.

$$x^{2}+34x-24=\left(x-\left(\sqrt{313}-17\right)\right)\left(x-\left(-\sqrt{313}-17\right)\right)$$

Evaluate

$$x^{2}+34x-24$$