# How do you factor 25a ^ { 2} - 45a + 18?

May 13, 2018

$\left(5 x - 6\right) \left(5 x - 3\right)$

#### Explanation:

$25 {a}^{2} - 45 a + 18$ = $25 {x}^{2} - 45 x + 18$ which is in the general form $a {x}^{2} + b x + c$
(i changed the a to x so that the general form would work)

You can either use the "cross" method or the quadratic formula.

So for the quadratic formula which is

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x = \frac{45 \pm \sqrt{{45}^{2} - 4 \cdot 25 \cdot 18}}{2 \cdot 25}$

$x = \frac{45 \pm \sqrt{225}}{50}$

$x = \frac{45 \pm 15}{50}$

$x = \frac{45 + 15}{50}$ or $x = \frac{45 - 15}{50}$

$x = \frac{60}{50}$ or $x = \frac{30}{50}$

$x = \frac{6}{5}$ or $x = \frac{3}{5}$

$25 {x}^{2} - 45 x + 18 = \left(x - \frac{6}{5}\right) \left(x - \frac{3}{5}\right) = \left(5 x - 6\right) \left(5 x - 3\right)$