SOLUTION: "what are the values of a and c in the trinomial square ax^2+12x+c if a is not 1 and c is greater than a?"

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Question 183214: "what are the values of a and c in the trinomial square ax^2+12x+c if a is not 1 and c is greater than a?"
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If ax%5E2+%2B+12x+%2B+c is a square, it can be expressed as
(1) %28sqrt%28a%29%2Ax+%2B+sqrt%28c%29%29%5E2
performing the square, I get
ax%5E2+%2B+2%2Asqrt%28a%29%2Asqrt%28c%29%2Ax+%2B+c
ax%5E2+%2B+sqrt%284ac%29%2Ax+%2B+c
Comparing this with
ax%5E2+%2B+12x+%2B+c
12+=+sqrt%284ac%29
square both sides
144+=+4ac
ac+=+36
c+=+36%2Fa
c should be a perfect square
If c+%3E+a,
a+=+4 and
9+=+36%2F4 is the only possibility
ax%5E2+%2B+12x+%2B+c+=+4x%5E2+%2B+12x+%2B+9 answer