so a perfect square trinomial like [tex]\bf \begin{array}{cccccllllll}
{{ a}}^2& + &2{{ a}}{{ b}}&+&{{ b}}^2\\
\downarrow && &&\downarrow \\
{{ a}}&& &&{{ b}}\\
&\to &({{ a}} + {{ b}})^2&\leftarrow
\end{array}\qquad
% perfect square trinomial, negative middle term
\begin{array}{cccccllllll}
{{ a}}^2& - &2{{ a}}{{ b}}&+&{{ b}}^2\\
\downarrow && &&\downarrow \\
{{ a}}&& &&{{ b}}\\
&\to &({{ a}} - {{ b}})^2&\leftarrow
\end{array}[/tex]
has its middle term, by multiplying 2 * the left guy * the right guy
so.. .let's see your equation now x² - 3x +n
so.. the middle term is 3x, neverminding the sign
[tex]\bf 2\cdot \sqrt{x^2}\cdot \sqrt{n}=3x\implies 2x\sqrt{n}=3x\implies \sqrt{n}=\cfrac{3x}{2x}
\\\\\\
\sqrt{n}=\cfrac{3}{2}\implies n=\left( \cfrac{3}{2} \right)^2\implies n=\cfrac{3^2}{2^2}\implies n=\cfrac{9}{4}[/tex]
