Section 2.5 : Quadratic Equations - Part I
1. Solve the following quadratic equation by factoring.
\[{u^2} - 5u - 14 = 0\]Show All Steps Hide All Steps
Start SolutionNot much to this problem. We already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.
\[\left( {u + 2} \right)\left( {u - 7} \right) = 0\] Show Step 2Now all we need to do is use the zero factor property to get,
\[\begin{array}{*{20}{c}}{u + 2 = 0}\\{u = - 2}\end{array}\hspace{0.25in}{\mbox{OR}}\hspace{0.25in}\begin{array}{*{20}{c}}{u - 7 = 0}\\{u = 7}\end{array}\]Therefore the two solutions are : \(\require{bbox} \bbox[2pt,border:1px solid black]{{u = - 2\,\,{\mbox{and }}u = 7}}\)
We’ll leave it to you to verify that they really are solutions if you’d like to by plugging them back into the equation.