Solving for X in a 60x^2 - 90x^4 Equation

[ziddy83]

hi, I was wonderin how i would solve for X in the following equation...

$$0 = 60x^2 - 90x^4$$

If i do add 90x^4 from both sides...and then go about solving for x, i get 1/x, which is the same as -x...and then i have to take the square root of a number, and i can't do that with a negative number. So.. yeah, i need help. my algebra skills are very rusty...thanks

 

[Hurkyl]

Maybe writing out your steps would help...


P.S., instead of dividing by an indeterminate quantity, it's usually better to factor it out.

 

[ziddy83]

as you wish........

90x^4 - 60^2
1.5x^4 = x^2
1.5 = 1/(x^2)
1.5 = -x^2
the negative root?

 

[Hurkyl]

I don't like your last step. $-x^2 = 1 / x^2$ is never right.

 

[robert Ihnot]

As Ziddy83 is trying to pointing out AB = 0 implies A =0 or B=0. (Reams have been written on that kind of stuff) so if we divide by 30X^2, we arrive at a much simpler equation to work with.

 

[JonF]

robert Ihnot as long as x is not = 0


try this:
$$0 = 60x^2 - 90x^4$$
$$0 = (2 - 3x^2)30x^2$$

 

[robert Ihnot]

JonF: robert Ihnot as long as x is not = 0. OF COURSE! And if x IS ZERO, well then that's an answer too!

 

[ziddy83]

in which step do i divide by 30x^2? right when i divide by 60x^2?

 

[ziddy83]

i knew there was factoring involved, i just couldn't get it to factor right, but then i still have to divide both sides, and dividing zero?

 

[ziddy83]

ahh perfect, dividing by 30x works just fine, but i still have the negative there?

 

[robert Ihnot]

Then you want to solve for that factor. Look again at JonF.

 

[ziddy83]

ok...gracias

 

[JonF]

You should never divide by 30x^2 as hurkyl suggested.


If you are with me up to: $$0 = (2 - 3x^2)30x^2$$...

When two quantities multiplied together equal zero that implies that one or both of them is zero.

So you have 30x^2 being multiplied to (2-3x^2).

This implies that if 30x^2 = 0 it would be a solution to your equation.

But also if 2-3x^2=0 that would also be a solution to your equation.



You can also think of it this way: You 30x^2 multiplied to some garbage, but it isn’t going to mater what that garbage is if 30x^2 = 0, likewise you also have 2-3x^2 being multiplied to some junk. Who cares what that junk is if 2-3x^2=0, because than that junk is being multiplied by zero, and anything multiplied by zero is zero.