Question

Solve the following quadratic equation by completing the square method.

 m² – 5m = –3

Answer 1

m² – 5m = –3

\[\Rightarrow m^2 - 5m + \left( \frac{- 5}{2} \right)^2 - \left( \frac{- 5}{2} \right)^2 = - 3\]

\[ \Rightarrow \left( m^2 - 5m + \frac{25}{4} \right) - \frac{25}{4} = - 3\]

\[ \Rightarrow \left( m - \frac{5}{2} \right)^2 = - 3 + \frac{25}{4}\]

\[ \Rightarrow \left( m - \frac{5}{2} \right)^2 = \frac {-12 + 25}{4}\]

\[ \Rightarrow \left( m - \frac{5}{2} \right)^2 = \frac{13}{4}\]

\[ \Rightarrow \left( m - \frac{5}{2} \right)^2 = \left( \frac{\sqrt{13}}{2} \right)^2 \]

\[ \Rightarrow m - \frac{5}{2} = \frac{\sqrt{13}}{2} \text{ or }  m - \frac{5}{2} = - \frac{\sqrt{13}}{2}\]

\[ \Rightarrow m = \frac{\sqrt{13}}{2} + \frac{5}{2} \text{ or } m = - \frac{\sqrt{13}}{2} + \frac{5}{2}\]

\[ \Rightarrow m = \frac{\sqrt{13} + 5}{2} \text{ or } m = \frac{5 - \sqrt{13}}{2}\]