What is the value that would make x2 -2x+c a perfect square trinomial.

Question

What is the value that would make x² -2x+c a perfect square trinomial. And how you got that answer if don't mind telling me so it could help me with future problems, thank you!!

c=

Answer 1

Perfect square trinomials are in the form of (a²+2ab+b²). In your case, a = x. Then we know that the second term, 2ab needs to equal -2x. Setting those two equal and solving for b = -1. Then c = b² . So (-1)² = 1

C=1. I hope that helps!

Answer 2

take half the x coefficient and square it

-2/2 = -1, squared = 1

add 1l and subtract 1

x^2-2x + 1 + c-1

(x-1)^2 + c-1

to get a perfect square c=1, then

(x-1)^2 +0 =

a perfect square (x-1)^2 = x^2-2x+c = x^2+2x+1