Find the solutions of the quadratic equation: $x^{2} + 6 x + 5 = 0$ .

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Solution

$x^{2} + 6 x + 5$
$\Rightarrow x^{2} + 5 x + x + 5$
$= x (x + 5) + 1 (x + 5)$
$= (x + 5) (x + 1)$
Therefore, the given quadratic equation becomes
$(x + 5) (x + 1) = 0$
This gives $x = - 5$ or $x = - 1$
Therefore, $x = - 1, - 5$ are the required solutions of the given equation.

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