deletions | additions       diff --git a/untitled.tex b/untitled.tex  index de9aecf..93cb758 100644  --- a/untitled.tex  +++ b/untitled.tex 
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&\iff (f^{2}+g^{2})+(fd-eg)+b=0\\  &\iff f^{2}+fd+g^{2}-eg+b=0\\  &\iff (f+\frac{1}{2}d)^{2}-\frac{1}{4}d^{2}+(g-\frac{1}{2})^{2}-\frac{1}{4}e^{2}=0 \text{ (By completing the square)}\\  &\iff (f+\frac{1}{2}d)^{2}+(g-\frac{1}{2}e)^2=\frac{1}{4}d^{2}+\frac{1}{4}e^{2} (f+\frac{1}{2}d)^{2}+(g-\frac{1}{2}e)^2=\frac{1}{4}d^{2}+\frac{1}{4}e^{2}\\  &\iff(f+\frac{1}{2}d)^{2}+(g-\frac{1}{2}e)^2=\frac{1}{4}(d^{2}+e^{2})  \end{align}  \end{proof}