How do you find the value of c that makes #x^2+26x+c# into a perfect square?

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Answer 1 · 2018-06-09T17:07:57

#c=169#

square is #(x+13)^2#

In the form:

#ax^2 +bx+c#

to complete the square #a=1# is required.

#c = (b/2)^2#

the square term is #b/2#

#x^2+26x+c#

#a=1# so we are okay to complete the square.

#b=26#

#c=(26/2)^2=13^2=169#

finally to complete the square:

#x^2+26x+169=(x+b/2)^2 = (x+13)^2#