Solve b^2+13b-36

$${ b }^{ 2 } +13b-36$$

Factor

$$\left(b-\frac{-\sqrt{313}-13}{2}\right)\left(b-\frac{\sqrt{313}-13}{2}\right)$$

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.

$$b^{2}+13b-36=0$$

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.

$$b=\frac{-13±\sqrt{13^{2}-4\left(-36\right)}}{2}$$

Square 13.

$$b=\frac{-13±\sqrt{169-4\left(-36\right)}}{2}$$

Multiply -4 times -36.

$$b=\frac{-13±\sqrt{169+144}}{2}$$

Add 169 to 144.

$$b=\frac{-13±\sqrt{313}}{2}$$

Now solve the equation b=\frac{-13±\sqrt{313}}{2} when ± is plus. Add -13 to \sqrt{313}.

$$b=\frac{\sqrt{313}-13}{2}$$

Now solve the equation b=\frac{-13±\sqrt{313}}{2} when ± is minus. Subtract \sqrt{313} from -13.

$$b=\frac{-\sqrt{313}-13}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-13+\sqrt{313}}{2} for x_{1} and \frac{-13-\sqrt{313}}{2} for x_{2}.

$$b^{2}+13b-36=\left(b-\frac{\sqrt{313}-13}{2}\right)\left(b-\frac{-\sqrt{313}-13}{2}\right)$$

Evaluate

$$b^{2}+13b-36$$