Solve: x^2+12 x+20 - Vidyadip

Question

Solve: $x^2+12 x+20$

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Answer

$x^2+12 x+20=x^2+12 x+\left(\frac{12}{2}\right)^2-\left(\frac{12}{2}\right)^2+20\left[\text { Adding and subtractiong }\left(\frac{12}{2}\right)^2, \text { that is } 6^2\right]$
$=x^2+12 x+6^2-6^2+20$
$\left.=(x+6)^2-16 \text { [comleting the square }\right]$
$=(x+6)^2-4^2$
$=[(x+6)-4][(x+6)+4]$
$=(x+6-4)(x+6+4)$
$=(x+2)(x+10)$

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