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Home / Algebra / Solving Equations and Inequalities / Quadratic Equations - Part I
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Section 2.5 : Quadratic Equations - Part I

1. Solve the following quadratic equation by factoring.

\[{u^2} - 5u - 14 = 0\]

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Start Solution

Not 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 2

Now 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.