SOLUTION: 3x^2+12x+5=p(x+q)^2+r Find the values of p,q and r

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Question 363908: 3x^2+12x+5=p(x+q)^2+r
Find the values of p,q and r
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2%2B12x%2B5=p%28x%2Bq%29%5E2%2Br Start with the given equation.


3x%5E2%2B12x%2B5=p%28x%5E2%2B2qx%2Bq%5E2%29%2Br FOIL



3x%5E2%2B12x%2B5=px%5E2%2B2pqx%2Bpq%5E2%2Br Distribute.


Notice that the coefficients for the x%5E2 terms are 3 (on the left) and p (on the right). So p=3


So the equation becomes 3x%5E2%2B12x%2B5=3x%5E2%2B2%2A3qx%2B3q%5E2%2Br


3x%5E2%2B12x%2B5=3x%5E2%2B6qx%2B3q%5E2%2Br Multiply


Now notice that the coefficients for the x terms are 12 and 6q. So 6q=12, which means that q=2


So the equation then becomes 3x%5E2%2B12x%2B5=3x%5E2%2B6%2A2x%2B3%282%29%5E2%2Br and simplifies to 3x%5E2%2B12x%2B5=3x%5E2%2B12x%2B12%2Br


Finally, we see that 12+r=5, which means that r=-7