Question 125945
x^2-x+1/4

= (x-(1/2))^2
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You recognize that x^2 and (1/4) are both perfect squares.
Then you regognize that 1 is twice the square root of (1/4)
Therefore the trinomial is a perfect square trinomial 
and factors as (a-b)^2
Your a is "x"; Your b is "1/2"
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Cheers,
Stan H.