Question

Solve the following quadratic equation by completing the square method.

x² + 2x – 5 = 0

Answer 1

x² + 2x – 5 = 0 

\[\Rightarrow x^2 + 2x + \left( \frac{2}{2} \right)^2 - \left( \frac{2}{2} \right)^2 - 5 = 0\]
\[ \Rightarrow \left( x^2 + 2x + 1 \right)  (- 1 - 5) = 0\]
\[ \Rightarrow \left( x + 1 \right)^2 (- 6) = 0\]
\[ \Rightarrow \left( x + 1 \right)^2 = 6\]
\[ \Rightarrow \left( x + 1 \right)^2 = \left( \sqrt{6} \right)^2 \]
\[ \Rightarrow x + 1 = \sqrt{6} \text{ or } x + 1 = - \sqrt{6}\]
\[ \Rightarrow x = \sqrt{6} - 1 \text{ or } x = - \sqrt{6} - 1\]