Algebra - Quadratic Equations

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Section 2.5 : Quadratic Equations - Part I

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5. Solve the following quadratic equation by factoring.

\[6{w^2} - w = 5\]

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The first thing we need to do is get everything on one side of the equation and then factor the quadratic.

\[\begin{align*}6{w^2} - w - 5 & = 0\\ \left( {6w + 5} \right)\left( {w - 1} \right) & = 0\end{align*}\] Show Step 2

Now all we need to do is use the zero factor property to get,

\[\begin{array}{*{20}{c}}{6w + 5 = 0}\\{\displaystyle w = - \frac{5}{6}}\end{array}\hspace{0.25in}{\mbox{OR}}\hspace{0.25in}\begin{array}{*{20}{c}}{w - 1 = 0}\\{w = 1}\end{array}\]

Therefore the two solutions are : \(\require{bbox} \bbox[2pt,border:1px solid black]{{w = - \frac{5}{6}\,\,{\mbox{and }}w = 1}}\)

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.