Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 151721: What is the actual quadratic formula, and how would you actually get the quation itself? All formulas have a reason to how it was made. Such as, a stated theorem.
This is an any book question. : What is the actual quadratic formula, and how would you actually get the quation itself? All formulas have a reason to how it was made. Such as, a stated theorem.
This is an any book question.
Answer by ankor@dixie-net.com(4539) About Me  (Show Source):
You can put this solution on YOUR website!
What is the actual quadratic formula, and how would you actually get the equation itself? All formulas have a reason to how it was made. Such as, a stated theorem.
:
consider ax^2 = bx + c = 0
:
solve this by completing the square of the left side, we have:
x^2 + (b/a)x + (c/a) = 0
;
adding -c/a to both sides and completing the square on the left side:
x^2 + (b/a)x + (b^2/(4a^2)) = (b^2/(4a^2)) - (c/a)
:
Now if we factor the left side, using the square root property
(x +(b/(2a)))^2 = (b^2-4ac)/(4a^2)
Finding the square root of both sides
x +(b/(2a)) = +/-sqrt((b^2-4ac)/(4a^2))
:
x = (-b/(2a)) +/- sqrt(b^2-4ac)/(2a)
We end up with the famous quadratic formula, that we all love so well!
x = (-b +- sqrt( b^2-4*a*c ))/(2*a)