Asked by Sylvestre Felis
How is the quadratic formula derived from the quadratic equation?
Answers
Answered by
Steve
ax^2 + bx + c = 0
a(x^2 + b/a x) = -c
x^2 + b/a x = -c/a
x^2 + b/a x + (b/2a)^2 = (b/2a)^2 - c/a
(x + b/2a)^2 = b^2/4a^2 - c/a
(x + b/2a)^2 = (b^2-4ac)/4a^2
x + b/2a = ±√(b^2-4ac)/2a
x = [-b±√(b^2-4ac)]/2a
a(x^2 + b/a x) = -c
x^2 + b/a x = -c/a
x^2 + b/a x + (b/2a)^2 = (b/2a)^2 - c/a
(x + b/2a)^2 = b^2/4a^2 - c/a
(x + b/2a)^2 = (b^2-4ac)/4a^2
x + b/2a = ±√(b^2-4ac)/2a
x = [-b±√(b^2-4ac)]/2a
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