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Section 2.5 : Quadratic Equations - Part I
3. Solve the following quadratic equation by factoring.
\[{y^2} = 11y - 28\]Show All Steps Hide All Steps
Start SolutionThe first thing we need to do is get everything on one side of the equation and then factor the quadratic.
\[\begin{align*}{y^2} - 11y + 28 & = 0\\ \left( {y - 4} \right)\left( {y - 7} \right) & = 0\end{align*}\] Show Step 2Now all we need to do is use the zero factor property to get,
\[\begin{array}{*{20}{c}}{y - 4 = 0}\\{y = 4}\end{array}\hspace{0.25in}{\mbox{OR}}\hspace{0.25in}\begin{array}{*{20}{c}}{y - 7 = 0}\\{y = 7}\end{array}\]Therefore the two solutions are : \(\require{bbox} \bbox[2pt,border:1px solid black]{{y = 4\,\,{\mbox{and }}y = 7}}\)
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.