Question

Find the value of c that makes the expression a perfect square trinomial x^2+15x+c

Answer 1

You take half the coefficient of the 'x' variable...and square it

so here....15/2 = 7.5 and 7.5^2 = 56.25

so we need to add 56.25

\[\large x^2 + 15x + 56.25\]

Now we just check to see if that can be factored...if it is a perfect square we should be able to write

\[\large (x + 7.5)(x + 7.5)\]

Does that work out? lets check by distributing

\[\large x^2 + 7.5x + 7.5x + 56.25\]
\[\large x^2 + 15x + 56.25\]

it works out