Question

what is c that makes this a perfect square? x^2+5x+c?

Answer 1

what to you get if you expand ( y + 2.5)^2 ?

Answer 2

\[(a+b)^2 = a^2+2ab+b^2\]

Answer 3

consider the perfect square of: (x+b)(x+b) = x^2 +2bx + b^2, and compare that to the given equation

Answer 4

if 2b = 5

and c = b^2

id solve for b, and square it

Answer 5

that doesnt make sense

Answer 6

then you need to go back a few chapters and relearn some stuff ....

Answer 7

walk me through it?

Answer 8

had to get to class :)

there are general trinomials: ax^2 + bx + c

but what makes a trinomial a perfect square is when it can be produced from expanding a binomial squared.

(x+b) is a binomial, 2 terms; when we square this ... when we multiply it by itself .... we produce a perfect square trinomial.

(x+b)^2 = (x+b)(x+b) = x^2 + 2bx + b^2. All perfect square trinomials take this form

Answer 9

so we only need to compare your specific problem with the general setup and see what needs to be adjusted.

x^2 + 2bx + b^2
x^2 + 5 x + c

notice by comparing the forms, that the value of c will have to equal b^2 ... whatever "b" may be.

we see that 2b compares to 5, this gives us an equation to solve: 2b=5

when we know what b has to be, then we know what b^2 has to be, and then since b^2 = c, we will know what c has to be .