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Quadratic Equations in One Variable — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsQuadratic Equations in One Variable2 Marks
Question
Solve equation by factorization : $3(x – 2)^2 = 147$
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Answer

$3(x – 2)^2 = 147$
$3(x^2 - 4x + 4) = 147$
$\Rightarrow 3x^2 - 12x + 12 - 147 = 0$
$\Rightarrow 3x^2 - 12x - 135 = 0$
$\Rightarrow x^2 - 4x - 45 = 0 ...$ (dividing by $3$)
$\Rightarrow x^2 - 9x + 5x - 45 = 0$
$\Rightarrow x(x - 9) + 5(x - 9) = 0$
$\Rightarrow (x - 9) (x + 5) = 0$
EIther $x - 9 = 0,$
then $x = 9$
or
$x + 5 = 0,$
then $x = -5$
Hence $x = 9, -5.$

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