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

Jun 9, 2018

$c = 169$

square is ${\left(x + 13\right)}^{2}$

#### Explanation:

In the form:

$a {x}^{2} + b x + c$

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

$c = {\left(\frac{b}{2}\right)}^{2}$

the square term is $\frac{b}{2}$

${x}^{2} + 26 x + c$

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

$b = 26$

$c = {\left(\frac{26}{2}\right)}^{2} = {13}^{2} = 169$

finally to complete the square:

${x}^{2} + 26 x + 169 = {\left(x + \frac{b}{2}\right)}^{2} = {\left(x + 13\right)}^{2}$