SOLUTION: How do you solve the problem 3x^2-15x-7=0 using complete the square?

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Question 992366: How do you solve the problem 3x^2-15x-7=0 using complete the square?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2-15x-7=0... group first two terms together

%283x%5E2-15x%29-7=0...factor out 3

3%28x%5E2-5x%29-7=0.........complete the square of %28x%5E2-5x%29

to do it, recall that %28a-b%29%5E2=a%5E2-2ab%2Bb%5E2
so, we need to add b%5E2 inside parentheses then subtract it outside parentheses
we do not know b, but we know a=1 and 2ab=5 and we can find b

2ab=5=>2%2A1%2Ab=5=>b=5%2F2 and b%5E2=%285%2F2%29%5E2
now add it to 3%28x%5E2-5x%29-7=0, and do not forget to multiply by 3 ones you subtract %285%2F2%29%5E2 because 3 is in front of parentheses

3%28x%5E2-5x%2B%285%2F2%29%5E2%29-3%285%2F2%29%5E2-7=0

3%28x-%285%2F2%29%5E2%29-3%2825%2F4%29-7=0

3%28x-%285%2F2%29%5E2%29-75%2F4-7=0

3%28x-%285%2F2%29%5E2%29-%2875%2F4%2B7%2A4%2F4%29=0

3%28x-%285%2F2%29%5E2%29-%2875%2F4%2B28%2F4%29=0

3%28x-5%2F2%29%5E2-103%2F4=0