# How do you find the missing number or term to make a perfect square trinomial. x^2 + 10x + c ?

Jun 7, 2015

A perfect square trinomial would be $\textcolor{b l u e}{{a}^{2}} + \textcolor{p u r p \le}{2 a b} + \textcolor{red}{{b}^{2}}$

Here : $\textcolor{b l u e}{a = x}$
$\textcolor{p u r p \le}{2 a b = 10 x}$
And $\textcolor{red}{{b}^{2} = c}$

Thus :

$\textcolor{b l u e}{a} \textcolor{red}{b} = 5 x$ ( we divide by $2$ on bothside )
$\textcolor{b l u e}{x} \cdot \textcolor{red}{b} = 5 x$ ( since $\textcolor{b l u e}{a = x}$ )
$\cancel{x} \cdot \textcolor{red}{b} = \cancel{x} \cdot 5$
$\textcolor{red}{b = 5}$

And thus :

color(red)(c=b^2=5^2=25