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

  • Thread starter ziddy83
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In summary, to solve for x in the equation 0 = 60x^2 - 90x^4, you can factor out 30x^2 from both sides to get 0 = (2 - 3x^2)30x^2. This means that either 30x^2 = 0 or 2 - 3x^2 = 0. Solving for x in each case, we get x = 0 or x = ±√(2/3). Therefore, the solutions to the equation are x = 0, x = √(2/3), or x = -√(2/3). It is important to note that dividing by an ind
  • #1
ziddy83
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hi, I was wonderin how i would solve for X in the following equation...

[tex] 0 = 60x^2 - 90x^4 [/tex]

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
 
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  • #2
Maybe writing out your steps would help...


P.S., instead of dividing by an indeterminate quantity, it's usually better to factor it out.
 
  • #3
as you wish........

90x^4 - 60^2
1.5x^4 = x^2
1.5 = 1/(x^2)
1.5 = -x^2
the negative root?
 
  • #4
I don't like your last step. [itex]-x^2 = 1 / x^2[/itex] is never right.
 
  • #5
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.
 
  • #6
robert Ihnot as long as x is not = 0


try this:
[tex] 0 = 60x^2 - 90x^4 [/tex]
[tex] 0 = (2 - 3x^2)30x^2 [/tex]
 
Last edited:
  • #7
JonF: robert Ihnot as long as x is not = 0. OF COURSE! And if x IS ZERO, well then that's an answer too!
 
  • #8
in which step do i divide by 30x^2? right when i divide by 60x^2?
 
  • #9
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?
 
  • #10
ahh perfect, dividing by 30x works just fine, but i still have the negative there?
 
  • #11
Then you want to solve for that factor. Look again at JonF.
 
  • #12
ok...gracias
 
  • #13
You should never divide by 30x^2 as hurkyl suggested.


If you are with me up to: [tex] 0 = (2 - 3x^2)30x^2 [/tex]...

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.
 

1. How do I solve for X in a 60x^2 - 90x^4 equation?

To solve for X in this equation, we can use the quadratic formula or factoring. First, we can rearrange the equation to be in the form ax^2 + bx + c = 0 where a = -90, b = 60, and c = 0. Then, we can plug these values into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Alternatively, we can factor out an x^2 term to get x^2(60 - 90x^2) = 0 and solve for x by setting each factor equal to 0.

2. Can this equation have multiple solutions for X?

Yes, this equation can have multiple solutions for X. It depends on the values of a, b, and c in the equation and which method of solving is used. For example, if we use the quadratic formula, we may get two solutions for X. If we use factoring, we may get three or more solutions.

3. What is the role of the coefficient of X^4 in this equation?

The coefficient of X^4, which is -90 in this equation, determines the shape of the graph of the equation. It tells us how wide or narrow the parabola will be and whether it will open upwards or downwards. In this case, the negative coefficient of X^4 means that the parabola will open downwards.

4. How can I check if my solution for X is correct?

To check if your solution for X is correct, you can plug it back into the original equation and see if it satisfies the equation. For example, if you solve for X and get X = 2, you can plug 2 into the equation and see if the left side equals the right side. If it does, then your solution is correct.

5. Can I use a graphing calculator to solve this equation?

Yes, you can use a graphing calculator to solve this equation. You can enter the equation into the calculator and use the "zero" or "root" function to find the solutions for X. This method may be helpful if the equation is difficult to solve algebraically.

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