Question
Solve the following quadratic equation by completing the square method.
m2 – 5m = -3
m2 – 5m = -3
✓
Answer
$\begin{array}{l}m^2-5 m+3=0 \\ \Rightarrow m^2-5 m+\frac{25}{4}-\frac{25}{4}+3=0 \text { (Adding and Subtracting } \frac{25}{4} \\ \Rightarrow\left(m^2-5 m+\frac{25}{4}\right)=\frac{25}{4}-3 \\ \Rightarrow\left(m-\frac{5}{2}\right)^2=\frac{25-12}{4} \\ \Rightarrow\left(m-\frac{5}{2}\right)^2=\frac{13}{4} \\ \Rightarrow m-\frac{5}{2}=\sqrt{\frac{13}{4}}\end{array}$
$\begin{array}{l}\Rightarrow m -\frac{5}{2}= \pm \frac{\sqrt{13}}{2} \\ \Rightarrow m -\frac{5}{2}=\frac{\sqrt{13}}{2} \text { or } m -\frac{5}{2}=-\frac{\sqrt{13}}{2} \\ \Rightarrow m =\frac{\sqrt{13}}{2}+\frac{5}{2} \text { or } m =-\frac{\sqrt{13}}{2}-\frac{5}{2} \\ \Rightarrow m =\frac{\sqrt{13}+5}{2} \text { or } m =\frac{-\sqrt{13}-5}{2}\end{array}$
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