SOLUTION: Starting with ax2 + bx + c = 0 and show each step to end up with:
x = - b + √b2 - 4ac
___________ ___________
2a
Algebra.Com
Question 113700: Starting with ax2 + bx + c = 0 and show each step to end up with:
x = - b + √b2 - 4ac
_______________________
2a
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Quadratic Formula Proven
Consider equation in a standard form
. What we want to do is complete the square, that is; note that , , and can be positive as well as negative. The right part of the equation should be .
get an equation like this:
(...)^2 = ...
Divide both parts by :
………..we will multiply and divide by
………..move to the right
………..
Now, if we want to of a out of here, we can to both sides of the equation:
………..
We did it so that the formula to the left would be a complete square of an expression:
………..
On the left side, there is a square of something, on the right, it is a number.
As you know, for all real numbers their squares are .
So if the number to the right happens to be , this means that that would satisfy this equation.
That's where the discriminat rule comes from.
Since the roots of equations like are , we have:
This quadratic formula can be simplified as:
open the bracket with :
divide and multiply the square root by :
get inside the square root as :
use distributive property:
Simplify:
Or
get 2a as the common denominator:
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