Chapter 9.4, Problem 10E

To determine

To find the value of c that completes the square.

  $x^2+9x+c$

Answer to Problem 10E

  $c=\frac{81}{4}$

Explanation of Solution

Given information:

Quadratic equation

  $x^2+9x+c$

Calculation:

Quadratic equation

  $x^2+9x+c\mathrm{........}(1)$

The general form of quadratic equation is $a{x}^2+bx+c$

For making quadratic equation perfect square adding ${\left(\frac{b}{2}\right)}^2$

Here

Adding ${\left(\frac{9}{2}\right)}^2$ in the equation $\left(1\right)$ without c

  $x^2+9x+{\left(\frac{9}{2}\right)}^2$

Comparing above equation with general quadratic equation

Then

  $c={\left(\frac{9}{2}\right)}^2$

On solving

  $c=\frac{81}{4}$

Therefore,

  $x^2+9x+\frac{81}{4}$ is a perfect square