SOLUTION: factoring: quadratic equations and completing the square 2a^2-5ab-3b^2=0 would i use complete the square to factor this? I'm not sure. Is there more than one way to do it?

Algebra ->  Square-cubic-other-roots -> SOLUTION: factoring: quadratic equations and completing the square 2a^2-5ab-3b^2=0 would i use complete the square to factor this? I'm not sure. Is there more than one way to do it?      Log On


   

Question 125943: factoring: quadratic equations and completing the square
2a^2-5ab-3b^2=0
would i use complete the square to factor this? I'm not sure. Is there more than one way to do it?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2a^2-5ab-3b^2=0
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Use the AC Method
Your Problem:
AC = 2*-3 = -6
B = -5
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Think of two numbers whose product = AC = -6
and whose sum is B = -5
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The numbers are -6 and +1
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Replace the B-term with the sum: -5ab = -6ab+ab to get:
2a^2-6ab+ab-3b^2 = 0
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Factor the 1st two terms and the last two terms separately to get:
2a(a-3b)+b(a-3b) = 0
Factor again to get:
(a-3b)(2a+b) = 0
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At this point you have factored the left side of the original equation.
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Therefore:
a = 3b or a = -b/2
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cheers,
stan H.