Solve the following equation for $x$ :
$x^{2} - 4 a x - b^{2} + 4 a^{2}$

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Solution

$x^{2} - 4 a x + b^{2} + 4 a^{2}$

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

$\Rightarrow x^{2} - 4 a x - [b^{2} - (2 a)^{2}] = 0$

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

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

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

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

$\Rightarrow x [x + (b - 2 a)] - (b + 2 a) [x + (b - 2 a)] = 0$

$\Rightarrow [x + (b - 2 a)] [x - (b + 2 a)] = 0$

$\Rightarrow x + b - 2 a = 0 o r x - (b + 2 a) = 0$

$\Rightarrow x = - (b - 2 a) o r x = b + 2 a .$

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

x^{2} - 4 a x + 4 a^{2} - b^{2} = 0 .

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

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