SOLUTION: How do you solve the following problem by factoring? 2a^2 = a + 15

Question 519905: How do you solve the following problem by factoring?
2a^2 = a + 15
Found 2 solutions by mananth, lmeeks54:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

m.ananth@hotmail.ca
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
This is pretty straightforward. The general method is to set all the terms on one side = to zero on the other side, then to factor the polynomial expression. Recall, you can do anything to either side of an equation as long as you do the same thing to the other side.
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Start with 2a^2 = a + 15
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If we subtract a + 15 from both sides, we can set the quadratic equation = 0
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2a^2 - (a + 15) = (a + 15) - (a + 15)
yields:
2a^2 - a - 15 = 0
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Now, set two aside two parentheses so that we have something that looks like:
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(__a + ?) (a - ?) = 0
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we need 2a^2, so we need a coefficient of 2 in front of one of the "a" terms:
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(2a + ?)(a - ?) = 0
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we need to get to -15 for the last term. The only factors of 15 are: 1, 15 or 3, 5. Either the 1 and 15 or the 3 and 5 are going to take the place of the "?" marks in our two factors. 1 and 15 aren't going to work because with one a negative and one a positive, we're never going to get to the -a term. However, with the 3 and 5 factors of 15, we can see how -3 x 2a would get us -6a and 5 x a would get us 5a and combining -6a + 5a would net us -a:
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(2a + 5)(a - 3) = 0
...check our work to make sure we factored this correctly:
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2a x a = 2a^2
2a x -3 = -6a
5 x a = 5a
5 x -3 = -15
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put this all together and we get:
2a^2 - a - 15 = 0
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so we factored the problem correctly. Now, to solve the equation, find the values of a in each factor (what's in the parentheses) to make the equation = 0
a = -2.5, 3 make the equation true:
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(2(-2.5) + 5)(-2.5 -3) = 0
(-5 + 5)(-5.5) = 0 (true, the first factor = 0)
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(2(3) + 5)(3 - 3) = 0
(6 + 5) (0) = 0 (true, the second factor = 0)
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the answers are a = -2.5 or 3
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cheers,
Lee

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