Solve the following quadric equations by factorization method only

$x^{2} + 1 = 0$

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Solution

$x^{2} + 1 = 0 \Rightarrow x^{2} i^{2} = 0 [∵ i^{2} = - 1] \Rightarrow (x + i) (x - i) = 0 [a^{2} - b^{2} = (a + b) (a - b)] \Rightarrow x = i, - i$

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