SOLUTION: For what real values of c is 9x^2 + 16x + c the square of a binomial? If you find more than one, then list your values in increasing order, separated by commas.

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Question 1085962: For what real values of c is 9x^2 + 16x + c the square of a binomial? If you find more than one, then list your values in increasing order, separated by commas.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Discriminant must be 0.

16%5E2-4%2A9%2Ac=0
4%2A4%2A16-4%2A9c=0
4%2A16-9c=0
9c=4%2A16
c=%284%2A16%29%2F9
highlight%28c=64%2F9%29





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---MISTAKE---
16%5E2-4%2A9%2A16%2Ac=0----mistake
16%2B36c=0
8%2B18c=0
4%2B9c=0
9c=-4
cross%28c=-4%2F9%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
9x%5E2+%2B+16x+%2B+c = 9%2A%28x%5E2+%2B+%2816%2F9%29%2Ax+%2B+c%2F9%29 = 9%2A%28x%2B8%2F9%29%5E2 + c%2F9 - 64%2F81%29  ===>

c%2F9 = 64%2F81  ====>  c = 64%2F9.


Check.  9x%5E2+%2B+16x+%2B+64%2F9 = 9%2A%28x%5E2+%2B+%2816%2F9%29%2Ax+%2B+64%2F81%29 = 9%2A%28x%2B8%2F9%29%5E2 = %283x+%2B+8%2F3%29%5E2.

The solution by "josgarithmetic" is WRONG.


For your safety, ignore it.