The perfect square is a number that is the product of two identical numbers. So 9 is a perfect square because it's the product of 3 * 3. For variables, perfect squares can be expressed as [tex](x+a)^{2}[/tex] or [tex](x-a)^{2}[/tex], where a is some number and x is the variable.
If we expand these terms, [tex](x+a)^{2}=x^{2}+2ax+a^{2}[/tex], and [tex](x-a)^{2}=x^{2}-2ax+a^{2}[/tex]. Since the given term is [tex]x^{2}+10x[/tex], we can see that it's part of the perfect square [tex]x^{2}+2ax+a^{2}[/tex]. We just need to find [tex]a^{2}[/tex].
So, [tex]x^{2}+2ax+a^{2}=x^{2}+10x+a^{2}[/tex]. Notice that [tex]10=2a[/tex], so [tex]a=5[/tex]. So, the missing constant term is [tex]5^{2}=25[/tex]. The perfect square is [tex](x+5)^{2}[/tex].
