## AravindG 3 years ago what us completing the square method..i knew it but frgt can anyone help me ?

1. anonymous

do you want a demonstration?

2. AravindG

general involving a ,b c and if possible a demonstration also

3. AravindG

it seems this method is pretty useful for solving quadratics thats why i am revising it

4. anonymous

firstly.... you agree that $ax^2 + bx + c = 0$ that's the quadratic equation, yes?

5. AravindG

yep

6. anonymous

now..divide ALL terms by a...what do you get?

7. anonymous

where's the x?

8. AravindG

x^2+(b/a)x+(c/a)=0

9. anonymous

right

10. anonymous

now subtract c/a from both sides

11. AravindG

$x^2+(b/a)x=-c/a$

12. anonymous

good. now divide b/a by 2..what do you get?

13. AravindG

only b/a?

14. anonymous

yes... but don't touch the equation yet

15. anonymous

just divide b/a by 2

16. AravindG

$(x+b/2a)^2=(4c-b^2)/4a$

17. AravindG

4c+b^2 srry

18. anonymous

why is it - b^2

19. AravindG

4c+b^2 srry

20. anonymous

$x^2 + (\frac ba)x + \frac{b^2}{4a^2} = -\frac ca + \frac{b^2}{4a^2}$ $\implies (x + \frac ba)^2 = \frac{b^2 - 4ac}{4a^2}$ you rushed too fast

21. AravindG

i see

22. AravindG

thx

23. anonymous

now take the square root of both sides

24. anonymous

do you need further help?

25. AravindG

nop gt it

26. anonymous

okay then

27. AravindG

@lgbasallote can you tell me how we can say that this method will be easier when we have an arbitrary quadratic?i mean is there any relation btw a,b,c so that i can recognise "AHA I CAN USE COMPLETING THE SQUARE HERE INSTEAD OF OTHER METHODS!"

28. anonymous

you can use completing the square method anywhere