A perfect square trinomial has the following structure:
[tex]a^2\cdot x^2+2\cdot a\cdot b\cdot x+b^2[/tex]We were given the expression:
[tex]x^2-15x+c[/tex]By comparing both expressions we know that:
[tex]\begin{gathered} a=1 \\ 2\cdot a\cdot b=-15 \end{gathered}[/tex]We can replace the value of a on the second expression to find b.
[tex]\begin{gathered} 2\cdot1\cdot b=-15 \\ 2\cdot b=-15 \\ b=\frac{-15}{2}=-7.5 \end{gathered}[/tex]The value of c is:
[tex]\begin{gathered} c=b^2 \\ c=(-7.5)^2=56.25 \end{gathered}[/tex]Therefore the perfect square trinomial is:
[tex]x^2-15x+56.25[/tex]It can be written as the following binomial squared:
[tex]x^2-2\cdot7.5\cdot x+(7.5)^2=(x-7.5_{})^2[/tex]