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Question
\[x^2 + 2x + 5 = 0\]
Solution
We have:
\[x^2 + 2x + 2 = 0\]
\[ \Rightarrow x^2 + 2x + 1 + 1 = 0\]
\[ \Rightarrow x^2 + 2 \times x \times 1 + 1^2 - (i )^2 = 0\]
\[ \Rightarrow (x + 1 )^2 - (i )^2 = 0\]
\[ \Rightarrow (x + 1 + i) (x + 1 - i) = 0\]
\[\Rightarrow (x + 1 + i) = 0\] or \[(x + 1 - i) = 0\]
\[\Rightarrow x = - 1 - i\] or \[x = - 1 + i\]
Hence, the roots of the equation are
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