Chapter 9.5, Problem 18PPS

To determine

Find the value of c.

Answer to Problem 18PPS

  $c=\frac{169}{4}$

Explanation of Solution

Given Information: $x^2-13x+c$

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

Calculation:

  $x^2-13x+c$

So, simplify and make the factor of -13

  $x^2-\left(2\times x\times \frac{13}{2}\right)+c$  (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 $b=\frac{13}{2}$

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

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

Now, compare equation (1) and (2)

  $c={\left(\frac{13}{2}\right)}^2$

Hence,

  $c=\frac{169}{4}$