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Solving a Quadratic Equation by Completion of Squares Method

Solve the fol...

Question

Solve the following quadratic equation.
$4 x^{2} + 4 b x - (a^{2} - b^{2}) = 0$

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Solution

Consider the given equation.
$4 x^{2} + 4 b x - (a^{2} - b^{2}) = 0$
$4 x^{2} + 4 b x + b^{2} - a^{2} = 0$
$(2 x + b)^{2} - a^{2} = 0$
$(2 x + b - a) (2 x + b + a) = 0$
$2 x + b - a = 0$ Or $2 x + b + a = 0$
$x = \frac{a - b}{2}$ Or $x = - \frac{a + b}{2}$

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