Derive from the standard quadratic equation, the form of the quadratic solution
ax2+bx+c=0 : basic quadratic equation
a(x2 + bx/a) + c=0
a((x+b/2a)2 - b2/4a2) + c=0 (retain equation with only one x variable; compensate for b term squared out with term - b2/4a2, )
a(x+b/2a)2 - b2/4a + c= 0 (a cancels 4a2 to make 4a)
a(x+b/2a)2 = (b2-4ac)/4a (rewrite b2/4a - c)
(x+b/2a)2 = (b2-4ac)/4a2
(x+b/2a) = +/-(rootof(b2-4ac))/2a (square root gives +/- answers
x= (-b +/- (rootof(b2-4ac)))/2a (x term singled out and the quadratic soln is written)
JD
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