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

1. lgbasallote

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. lgbasallote

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

5. AravindG

yep

6. lgbasallote

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

7. lgbasallote

where's the x?

8. AravindG

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

9. lgbasallote

right

10. lgbasallote

now subtract c/a from both sides

11. AravindG

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

12. lgbasallote

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

13. AravindG

only b/a?

14. lgbasallote

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

15. lgbasallote

just divide b/a by 2

16. AravindG

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

17. AravindG

4c+b^2 srry

18. lgbasallote

why is it - b^2

19. AravindG

4c+b^2 srry

20. lgbasallote

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

21. AravindG

i see

22. AravindG

thx

23. lgbasallote

now take the square root of both sides

24. lgbasallote

do you need further help?

25. AravindG

nop gt it

26. lgbasallote

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. lgbasallote

you can use completing the square method anywhere