SOLUTION: Factor by using the zero product theorem and factoring.. 5a2 - 33a = 14

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Question 84267: Factor by using the zero product theorem and factoring..
5a2 - 33a = 14
Found 2 solutions by funmath, rapaljer:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by using the zero product theorem and factoring..
5a2 - 33a = 14
5a%5E2-33a-14=14-14
5a%5E2-33a-14=0 factor, I'm using the ac method, you can use the trial and error method as well.
5a%5E2-35a%2B2a-14=0
%285a%5E2-35a%29%2B%282a-14%29=0
5a%28a-7%29%2B2%28a-7%29=0
%285a%2B2%29%28a-7%29=0
Set each factor = to 0 and solve for a (zero product theorem)
5a+2=0 or a-7=0
5a+2-2=0-2 or a-7+7=0+7
5a=-2 or a=7
5a/5=-2/5 or a=7
a=-2/5 or a=7
Happy Calculating!!!!

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
5a%2A2+-+33a+=+14
5a%5E2+-33a+-+14=0

The hard part of this is the factoring of the trinomial since the coefficient of the a*2 is NOT 1. I call this "Advanced Trinomial Factoring", and I have a Lesson PLan for this topic in algebra.com, or go to my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for "MATH IN LIVING COLOR", "Basic Algebra", "Chapter 2", "Advanced Trinomial Factoring."

5a%5E2+-33a+-+14=0
%285a%2B2%29%28a-7%29+=+0+
%285a%2B2%29+=+0 or %28a-7%29=+0+
5a=-2 or a=7
a=+-2%2F5+ or a=7

R^2 at SCC