Lesson PROOF of quadratic formula by completing the square

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> Lesson PROOF of quadratic formula by completing the square     (Log On)
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This Lesson (PROOF of quadratic formula by completing the square) was created by by ichudov(332) About Me : View Source, Show
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Consider this quadratic equation: a*x^2+b*x+c=0
Try to use "completing the square":
add and subtract b^2/(4*a)
a*x^2+b*x+c+expr(b^2/(4*a))-expr(b^2/(4*a))=0
Rewrite the equation
(a*x^2+b*x+b^2/expr(4*a))-b^2/expr(4*a)+c=0
Factor for a
a*(x^2+b/a*x+b^2/(4*a^2))-b^2/(4*a)+c=0
Factor the complete square (x^2+b/a*x+b^2/(4*a^2))
(x^2+b/a*x+b^2/(4*a^2))=(x+b/(2*a))^2
a*(x+b/(2*a))^2-b^2/(4*a)+c=0
a*(x+b/(2*a))^2=b^2/(4*a)-c
a*(x+b/(2*a))^2=(b^2-4*a*c)/(4*a)
Multiply both sides by 1/a
(x+(b/(2*a)))^2=(b^2-4*a*c)/(4*a^2)
Take the square root for both sides
x+b/(2*a)=sqrt((b^2-4*a*c)/(4*a^2)) or x+b/(2*a)=-sqrt((b^2-4*a*c)/(4*a^2))
x=(-b)/(2*a)+sqrt(b^2-4*a*c)/(2*a) or x=(-b)/(2*a)-sqrt(b^2-4*a*c)/(2*a)
x=(-b+-sqrt(b^2-4*a*c))/(2*a)
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