# How do you factor 36x^2 + 35x + 8?

Jul 20, 2018

$36 {x}^{2} + 35 x + 8 = \left(72 x + 35 - \sqrt{73}\right) \left(72 + 35 + \sqrt{73}\right)$

#### Explanation:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ where the equation is $a {x}^{2} + b x + c = 0$

Therefore,
$a = 36$, $b = 35$ and $c = 8$

$x = \frac{- 35 \pm \sqrt{{35}^{2} - 4 \times 36 \times 8}}{2 \times 36}$

$x = \frac{- 35 \pm \sqrt{73}}{72}$

$x = \frac{- 35 + \sqrt{73}}{72}$ or $x = \frac{- 35 - \sqrt{73}}{72}$

$36 {x}^{2} + 35 x + 8$

=(x-((-35+sqrt73)/72))(x-(-35-sqrt73)/72))

$= \left(x + \frac{35}{72} - \frac{\sqrt{73}}{72}\right) \left(x + \frac{35}{72} + \frac{\sqrt{73}}{72}\right)$

$= \left(72 x + 35 - \sqrt{73}\right) \left(72 + 35 + \sqrt{73}\right)$