Question

What value of c makes x^2 +5x+c a perfect square.

Answer 1

To find a perfect square, all you need to do is divide the second coefficient by 2 (5 in this case) and then square it. In other words:

5/2=2.52. 5^2=6.25. Thus, x^2+5+6.25, and in factored form, (x+2.5)(x+2.5)

Hope this helps!

Answer 2

`Perfect\ square:a^2+2ab+b^2=(a+b)^2\\\\x^2+5x+c=x^2+2x\cdot2.5+c\\\\Th\e coclusion:c=2.5^2=6.25\\\\then\ x^2+5x+6.25=x^2+2x\cdot2.5+2.5^2=(x+2.5)^2`