Question

I need help please x^2 - 15x + c

Answer 1

A perfect square trinomial has the following structure:

`a^2\cdot x^2+2\cdot a\cdot b\cdot x+b^2`

We were given the expression:

`x^2-15x+c`

By comparing both expressions we know that:

`\begin{gathered} a=1 \\ 2\cdot a\cdot b=-15 \end{gathered}`

We can replace the value of a on the second expression to find b.

`\begin{gathered} 2\cdot1\cdot b=-15 \\ 2\cdot b=-15 \\ b=(-15)/(2)=-7.5 \end{gathered}`

The value of c is:

`\begin{gathered} c=b^2 \\ c=(-7.5)^2=56.25 \end{gathered}`

Therefore the perfect square trinomial is:

`x^2-15x+56.25`

It can be written as the following binomial squared:

`x^2-2\cdot7.5\cdot x+(7.5)^2=(x-7.5_{})^2`