How do you find the c that makes the trinomial #x^2+9x+c# a perfect square?
#(x+b/2)^2 = x^2+bx+b^2/4#
#c = b^2/4 = color(blue)(9)^2/4 = 81/4#
More generally, we find:
#ax^2+bx+c = a(x+b/(2a))^2+(c-b^2/(4a))#
#x^2+bx+c = (x+b/2)^2+(c-b^2/4)#
as in our example.
The pattern is:
Match the terms of the given equation with the right side of the pattern.
Match the terms of the given equation,
Matching the first terms:
Matching the second terms gives us the following equation:
We can use the above equation to solve for the value of "a" by dividing both sides of the equation by 2x:
Matching the constant terms, gives us the following equation:
This is your answer: