Solve each of the following quadratic equations:
$x^{2} + 12 x + 35 = 0$

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Solution

$x^{2} + 12 x + 35 = 0$

$x^{2} + (7 + 5) x + 35 = 0$

$x^{2} + 7 x + 5 x + 35 = 0$

$x (x + 7) + 5 (x + 7) = 0$

$(x + 7) (x + 5) = 0$

if $x + 7 = 0$ then $x = - 7$ and
if $x + 5 = 0$ then $x = - 5$

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