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:
|
|
|
