# How do you solve s^ { 2} - 14s + 45= 0?

Mar 13, 2017

$s = 9 , s = 5$

#### Explanation:

There are multiple ways of solving this. (The easiest in this case):

Find two numbers that when multiplied gives you $45$ and when added gives you $- 14$

This usually a trial and error process but you'll find that these two numbers are $- 9$ and $- 5$

When we multiply $- 9$ and $- 5$ we get $45$ and when we add $- 9$ and $- 5$ we get $- 14$

We can rewrite this information as $\left(s - 9\right) \left(s - 5\right) = 0$

We then have to solve for the variable $s$

We treat this as two separate equations such that:

$s - 9 = 0$ and $s - 5 = 0$

$s = 9 , s = 5$
Note: you can check your answer by multiplying out $\left(s - 9\right) \left(s - 5\right)$ and you should get what you started with.