Solve x^2+13x-64

$${ x }^{ 2 } +13x-64$$

Factor

$$\left(x-\frac{-5\sqrt{17}-13}{2}\right)\left(x-\frac{5\sqrt{17}-13}{2}\right)$$

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.

$$x^{2}+13x-64=0$$

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.

$$x=\frac{-13±\sqrt{13^{2}-4\left(-64\right)}}{2}$$

Square 13.

$$x=\frac{-13±\sqrt{169-4\left(-64\right)}}{2}$$

Multiply -4 times -64.

$$x=\frac{-13±\sqrt{169+256}}{2}$$

Add 169 to 256.

$$x=\frac{-13±\sqrt{425}}{2}$$

Take the square root of 425.

$$x=\frac{-13±5\sqrt{17}}{2}$$

Now solve the equation x=\frac{-13±5\sqrt{17}}{2} when ± is plus. Add -13 to 5\sqrt{17}.

$$x=\frac{5\sqrt{17}-13}{2}$$

Now solve the equation x=\frac{-13±5\sqrt{17}}{2} when ± is minus. Subtract 5\sqrt{17} from -13.

$$x=\frac{-5\sqrt{17}-13}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-13+5\sqrt{17}}{2} for x_{1} and \frac{-13-5\sqrt{17}}{2} for x_{2}.

$$x^{2}+13x-64=\left(x-\frac{5\sqrt{17}-13}{2}\right)\left(x-\frac{-5\sqrt{17}-13}{2}\right)$$

Evaluate

$$x^{2}+13x-64$$