SOLUTION: Perfect Square Trinomial m^2 + m + 1/4 I tried but my teacher never explained how to do one with a fraction! Please Help!

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Question 735007: Perfect Square Trinomial
m^2 + m + 1/4
I tried but my teacher never explained how to do one with a fraction! Please Help!
Found 2 solutions by MathLover1, josgarithmetic:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
m%5E2+%2B+m+%2B+1%2F4...write m%5E2 and m as 4m%5E2%2F4 and 4m%2F4

4m%5E2%2F4+%2B+4m%2F4+%2B+1%2F4.....factor out 1%2F4

%281%2F4+%29%284m%5E2%2B4m%2B1%29

%281%2F4%29+%282m%2B1%29%5E2

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You are trying to find (m+c)(m+c) so that the constant term is 1/4 and this must be c%5E2=1%2F4. This would mean, c=1%2F2. The question next is, will c=1/2 give you the m term that you need?

You see, you want this: %28m%2Bc%29%28m%2Bc%29=m%5E2%2Bmc+%2Bmc%2Bc%5E2
and m%5E2%2Bmc%2Bmc%2Bc%5E2=m%5E2%2B1%2Am%2B1%2F4.

You must have both, 2mc=m AND c%5E2=1%2F4%7D.++How+will+this+work%3F%0D%0AThe+2mc+means+that+%7B%7B%7B2c=1. The c^2 as from before means c=1%2F2. Using the 2c=1 result, solve for c and find c=1%2F2.

There it is. c=1%2F2.
m%5E2%2Bm%2B1%2F4=%28m%2B1%2F2%29%5E2.