Tuesday, 29 November 2011

C1 - Quadratic Equations - Completing the Square

Final method of solving quadratic equations is Completing the Square. By completing the square for :
 ax2 + bx + c, you will generate the Quadratic Formula by solving for x.

The general method consists of changing the quadratic in the form ax2 + bx + c into (x+d)2+ e =0

where d = b/2 and e = b2 / 4 
* This method requires a = 1, so if the coefficient of x is not 1 . Divide by a to get it to be 1.
* Then rewrite the Formula in the form shown above. Solve for x by :
1) Taking e to the otherside and squarerooting it, and then subtracting b.

My image notes show two examples. 1) How to derive the quadratic formula 2) A numerical example :

Completing the Square Notes

     
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