Chapter 9.5, Problem 13PPS

To determine

Find the value of c.

Answer to Problem 13PPS

  $c=169$

Explanation of Solution

Given Information: $x^2+26x+c$

Formula Used: $a^2+2ab+b^2={(a+b)}^2$

Calculation:

  $x^2+26x+c$

So, simplify and make the factor of 26

  $x^2+\left(2\times x\times 13\right)+c$  (1)

As, $a^2+2ab+b^2={(a+b)}^2$

Compare equation (1) with $a^2+2ab+b^2={(a+b)}^2$

  $a=x$ and $b=13$

Put value of a and b in $a^2+2ab+b^2={(a+b)}^2$

  $x^2+\left(2\times x\times 13\right)+{13}^2={(x+13)}^2$  (2)

Now, compare equation (1) and (2)

  $c={13}^2$

Hence,

  $c=169$