Answer
$(x+\frac{1}{2})^2$
Work Step by Step
$x^2+x+\frac{1}{4}$
$=x^2+\frac{x}{2}+\frac{x}{2}+\frac{1}{4}$
$=x(x+\frac{1}{2})+\frac{1}{2}(x+\frac{1}{2})$
$=(x+\frac{1}{2})(x+\frac{1}{2})$
$=(x+\frac{1}{2})^2$
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