123goldie 4 years ago How do you complete the square?

1. gandalfwiz

with lines

2. 123goldie

I mean with like quadratic equations...

3. Harkirat

u add square of half the coefficient of x to both sides.....

4. Harkirat

if u give a question I can explain..

5. 123goldie

Got it!

6. Harkirat

good for u then....☺

7. amistre64

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

8. amistre64

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

9. Diogo

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) )

10. Diogo

it will give you C = 25. Thats the number you were looking for ;)

11. Diogo

I've found this out by myself when i was in college. It was very useful for my advanced math classes

12. Diogo

I've found this out by myself when i was in college. It was very useful for my advanced math classes

13. Harkirat

25 = 5² which is square of half of the coefficient of x as I said !!!

14. Diogo

well.. here is the proof of what you said then. only words doesnt mean anything :p

15. gandalfwiz

could I have another example?

16. gandalfwiz

Just to get it in my brain :)

17. amistre64

abstract: ax^2 +bx +c c = (b/2)^2

18. Diogo

x^2 + 4x + C 4x = 2x*sqrt(C) 2 = sqrt(C) C = 4 so: x^2 + 4x + 4 = perfect square

19. amistre64

thats if a=1 i believe

20. gandalfwiz

thnx!

21. 123goldie

Thanks guys!

22. amistre64

no prob