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:

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

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