## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x=\left\{ -11,5 \right\}$
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{ equation }$ \begin{array}{l}\require{cancel} x^2+6x-55 \end{array} has $c= -55$ and $b= 6 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ 11,-5 \right\}.$ Using these two numbers, the $\text{ equation }$ above is equivalent to \begin{array}{l}\require{cancel} (x+11)(x-5)=0 .\end{array} Equating each factor to zero (Zero Product Property), and then isolating the variable, the solutions are $x=\left\{ -11,5 \right\} .$