# How do you find the value of c that makes x^2-13x+c into a perfect square?

Apr 13, 2017

$\frac{169}{4}$

#### Explanation:

Half the coefficient of x which would be $- \frac{13}{2}$ and then square it which would be $\frac{169}{4}$ which 'c' should be equal to.

The perfect square would be ${\left(x - \frac{13}{2}\right)}^{2}$

Apr 13, 2017

${x}^{2} - 13 x + 42.25$ is a perfect square.

#### Explanation:

This is the process called 'completing the square'

A quadratic trinomial is in the form $a {x}^{2} + b x + c$

To make a perfect square, add on ${\left(\frac{b}{2}\right)}^{2}$ as the $c$ term

In this case $b = - 13$

${x}^{2} - 13 x + {\left(\frac{- 13}{2}\right)}^{2}$ is a perfect square

${x}^{2} - 13 x + 42.25$

$= {\left(x - 6.5\right)}^{2}$