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\frac{x^{2}+4x+4}{2}
Factor out \frac{1}{2}.
\left(x+2\right)^{2}
Consider x^{2}+4x+4. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=x and b=2.
\frac{\left(x+2\right)^{2}}{2}
Rewrite the complete factored expression.