Question

what us completing the square method..i knew it but frgt can anyone help me ?

Answer 1

do you want a demonstration?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

yep

Answer 6

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

Answer 7

where's the x?

Answer 8

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

Answer 9

right

Answer 10

now subtract c/a from both sides

Answer 11

\[x^2+(b/a)x=-c/a\]

Answer 12

good.

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

Answer 13

only b/a?

Answer 14

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

Answer 15

just divide b/a by 2

Answer 16

\[(x+b/2a)^2=(4c-b^2)/4a\]

Answer 17

4c+b^2 srry

Answer 18

why is it - b^2

Answer 19

4c+b^2 srry

Answer 20

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

Answer 21

i see

Answer 22

thx

Answer 23

now take the square root of both sides

Answer 24

do you need further help?

Answer 25

nop gt it

Answer 26

okay then

Answer 27

@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!"

Answer 28

you can use completing the square method anywhere