Solve for k
k>-\frac{1}{4}
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4k^{2}+4k+1-4k^{2}>0
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2k+1\right)^{2}.
4k+1>0
Combine 4k^{2} and -4k^{2} to get 0.
4k>-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
k>-\frac{1}{4}
Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.
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