Here's the question you clicked on:
123goldie
How do you complete the square?
I mean with like quadratic equations...
u add square of half the coefficient of x to both sides.....
if u give a question I can explain..
in algebra we are given an equation; quadratic in nature usually; and in order to "complete the square" we can look to geometry: for instance: x^2 +6x + ??? completes the square set it up like this \begin{array}c &&&6/2\ xs\\ &x^2&x&x&x\\ &x&1&2&3\\ 6/2\ xs&x&4&5&6\\ &x&7&8&9\\ \end{array} it take an additional 9 pieces to "complete" the square
while the geometry is useful to describe what a "complete square" square is; it impractical to use all the time; so we take our lead from it and abstractly construct our square with half of our "x" coefficient; and square it
example: you have x^2 + 10x + C you want to find C. just simply solve this equation: \[10x = 2x*\sqrt{C}\] i mean, you have to match the second term with this expression ( 2x*sqrt(C) )
it will give you C = 25. Thats the number you were looking for ;)
I've found this out by myself when i was in college. It was very useful for my advanced math classes
I've found this out by myself when i was in college. It was very useful for my advanced math classes
25 = 5² which is square of half of the coefficient of x as I said !!!
well.. here is the proof of what you said then. only words doesnt mean anything :p
could I have another example?
Just to get it in my brain :)
abstract: ax^2 +bx +c c = (b/2)^2
x^2 + 4x + C 4x = 2x*sqrt(C) 2 = sqrt(C) C = 4 so: x^2 + 4x + 4 = perfect square
thats if a=1 i believe