Derive from the standard quadratic equation, the form of the quadratic solution

ax2+bx+c=0 : basic quadratic equation

a(x+ bx/a) + c=0  

a((x+b/2a)- 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 4ato 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)

 

Answered by Jaiveer D. Maths tutor

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