solve square

Neha · 2006-10-11 03:36:25

solve by completing the square:

3x^2 + x = -5
subtract x form both sides...

mathsyperson · 2006-10-11 03:56:42

Ooh, that's a nasty one. You're going to have some horrible fractions in there.

First you need to divide by 3 to just get a single x².
x² + x/3 = -5/3

Then you convert the left side into a perfect square plus a constant.
(x+1/6)² -1/36 = -5/3

Put the constant on the other side:
(x+1/6)² = -59/36

Square root both sides and subtract 1/6 to get x on its own:
x = ±√(-59/36) - 1/6

Simplify: x = (±√-59 - 1)/6

So there's your answer. Unfortunately, √-59 can't be done without going into imaginary numbers, which I'd imagine you're not doing yet, so you just write that there are no solutions.

You could also just show that the discriminant is negative at the start and then you wouldn't have to do any of that work.

Neha · 2006-10-11 04:34:03

Oh thanks alot for the help.
yeah that was a bit nasty i was checking in my book to see how tehy did it ...and then tryed the same way on this problem ...didnt work. i dont know why
anyways thanks

Toast · 2006-10-12 22:02:40

Hi everyone!

Lol mathysperson that's a very confusing way to solve for x, I don't even know what you're talking about. I woulda simply used the quadratic forumula:

since

so

(omg i can use latex now xD, it feels so good when the equation comes out right)

Last edited by Toast (2006-10-12 22:03:55)

mathsyperson · 2006-10-13 01:38:00

Payari wrote:

solve by completing the square:

I was just using the requested method is all. You're right, the quadratic equation is easier to use in general, but if you're asked to complete the square then you need to complete the square.

Incidentally, the quadratic formula is basically just a generalised version of the completing square method.

Neha · 2006-10-13 04:35:54

just like this one :
x^2 - 4x - 12 = 0

use the quadratic formula

-(-4) +- sqrt ( (-4)^2 - 4(1)(-12) )
-------------------------------------
2(-4)

4 +- sqrt ((-16) - 4(-48))
--------------------------
-8

4 +- sqrt ( (-16) - (-48) ) >>>>>> sqrt ( -16 + 48)
------------------------------- --------------------
-8 -8

4 +- sqrt (64)
----------------
8

now what...thats it or we have to do more?

polylog · 2006-10-13 05:02:31

Well, remember that 64 is a perfect square, so you can still simplify that!

luca-deltodesco · 2006-10-13 05:04:07

i.e.

Neha · 2006-10-13 05:08:54

thanks
but shouldnt it be
4 +- 8
--------
-8

then
-0.5 +- (-1)

mathsyperson · 2006-10-13 05:28:13

The denominator isn't -8, it's 2.

So then you've got 4+-8, which is 2+-4, which is -2 or 6.
-------
2

Just factorising it into (x+2)(x-6) at the start would be a lot easier though.

Neha · 2006-10-13 05:32:11

if its 2
so it would be
2 +- 4

Math Is Fun Forum

#1 2006-10-11 03:36:25

solve square

#2 2006-10-11 03:56:42

Re: solve square

#3 2006-10-11 04:34:03

Re: solve square

#4 2006-10-12 22:02:40

Re: solve square

#5 2006-10-13 01:38:00

Re: solve square

#6 2006-10-13 04:35:54

Re: solve square

#7 2006-10-13 05:02:31

Re: solve square

#8 2006-10-13 05:04:07

Re: solve square

#9 2006-10-13 05:08:54

Re: solve square

#10 2006-10-13 05:28:13

Re: solve square

#11 2006-10-13 05:32:11

Re: solve square

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