Solve the following equation by using the method of completing the square:
$4 x^{2} + 4 b x - (a^{2} - b^{2}) = 0$ [ 3 marks]

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Solution

$4 x^{2} + 4 b x - (a^{2} - b^{2}) = 0$

$4 x^{2} + 4 b x - a^{2} + b^{2} = 0$ [ 1 mark]

$(2 x)^{2} + 2. (2 x) . b + b^{2} - a^{2} = 0$ [1 mark]

$(2 x + b)^{2} - a^{2} = 0$
$(2 x + b + a) (2 x + b - a) = 0$
$x = \frac{- (b + a)}{2}$ or $x = \frac{a - b}{2}$ [ 1 mark]

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