Given data:
The given quadratic equation is x^2 -13x+5=0.
The given expression can be written as,
[tex]\begin{gathered} x^2-13x+5=0 \\ x^2-13x+5+(\frac{13}{2})^2-(\frac{13}{2})^2=0^{} \\ x^2-13x+5+\frac{169}{4}-\frac{169}{4}=0 \\ x^2-13x+\frac{169}{4}=\frac{169}{4}-5 \\ x^2-13x+\frac{169}{4}=\frac{149}{4} \\ (x-\frac{13}{2})^2=\frac{149}{4} \end{gathered}[/tex]Thus, add 169/4 on both sides to make perfect square.
