SOLUTION: Calculate the value of A,B and C for which 3x^2-6x+5=A (X+B)^2+C

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Question 1159487: Calculate the value of A,B and C for which 3x^2-6x+5=A (X+B)^2+C
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by MathLover1(20849) About Me  (Show Source):
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Calculate the value of A,B and C for which
3x%5E2-6x%2B5=A%28x%2BB%29%5E2%2BC
3x%5E2-6x%2B5=A%28x%5E2%2B2Bx%2BB%5E2%29%2BC
3x%5E2-6x%2B5=Ax%5E2%2B2ABx%2BAB%5E2%2BC-> comparing coefficients, we see that A=3,2AB=-6, and AB%5E2%2BC=5
if 2AB=-6 and A=3, then
2%2A3B=-6

6B=-6
B=-1
then AB%5E2%2BC=5->3%28-1%29%5E2%2BC=5->3%2A1%2BC=5->C=5-3->C=2
so, the value of A,B and C are:
A=3,B=-1 and 2

check:
3x%5E2-6x%2B5=3%28x-1%29%5E2%2B2
3x%5E2-6x%2B5=3%28x%5E2-2x%2B1%29%2B2
3x%5E2-6x%2B5=3x%5E2-6x%2B3%2B2
3x%5E2-6x%2B5=3x%5E2-6x%2B5-> true