How do you solve #5x ^ { 2} + 17x = 12#?
1 Answer
The quadratic function would always be a good option, but in this case factoring is sufficient - I like mental math so I find quickly running a few scenarios in the guess and test method works best.
Explanation:
Arrange the equation so that all terms equal 0
the integer 5 can only be factored by 1 & 5, this means that your polynomial will look something like this:
(5x +/- ? )(x +/- ? )
the number 12 can be factored into 1x12, 2x5, 3x4, etc.
Your next step is to figure out what combination of factors will yield a +17x as the middle term
Because the +17 is large value, I assume that our 5x will be multiplied by a positive integer when I foil - my first thought was:
(5x - 2) (x + 6) --> when I foil i get
... not the 17x in the central term I was looking for. but I got the first and third terms in the integer correct.
Then I tried:
(5x-3)(x+4) --> when foiled we get
:-)
the values for x that will equal zero from this factored answer would be 3/5, -4
ie. 5x -3 = 0 x+4 = 0
