Question

X^2-4αx+4α^2-β^2 quadratic equation by completing the sqaure

Answer 1

$x^{2} -4\alpha x+4\alpha^ {2} -\beta ^{2} = 0\\x^{2} -4\alpha x+(4\alpha^ {2} -\beta ^{2})=0\\(x)^{2} -2(x)(2\alpha)+(2\alpha)^{2} -\beta ^{2} =0\\(x-2\alpha)^{2} -\beta ^{2} =0\\(x-2\alpha)^{2}=\beta ^{2} \\(x-2\alpha)=\sqrt{\beta ^{2} } \\(x-2\alpha)=\beta ,-\beta\\ x= 2\alpha+\beta  , 2\alpha-\beta$