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

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Answer 1 · 2017-03-13T21:25:48

#s=9, s=5#

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 #(s-9)(s-5)=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#

Our final answer is therefore,

#s=9,s=5#

Note: you can check your answer by multiplying out #(s-9)(s-5)# and you should get what you started with.