2007-06-26 Completing The Square
ax2 + bx + c = 0
x2 + (b/a) x + (c/a) = 0
x2 + (2b/2a) x + (b2/4a2) - (b2/4a2) + (c/a) = 0
(x + b/2a)2 - (b2/4a2) + (c/a) = 0
(x + b/2a)2 = (b2/4a2) - (c/a)
(x + b/2a)2 = (b2-4ac) / (4a2)
x + b/2a = +- sqrt( (b2-4ac) / (4a2) )
x + b/2a = +- sqrt( b2-4ac ) / (2a)
x = (-b +- sqrt( b2 - 4ac )) / (2a)
Beautiful, isn't it?
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