Solving 12x^2 - 9 = 0: What to Do Next?

  • Thread starter Jimmy84
  • Start date
In summary, if you can't solve the problem, you can try the other one. If you still can't solve the problem, you can try finding a third option. Just keep solving.
  • #1
Jimmy84
191
0

Homework Statement



12x^2 - 9 = 0

Homework Equations





The Attempt at a Solution



Im having doubts about how to start


I could factorize for 3(4x^2 - 3) = 0

or to pass -9 to the other side 12x^2 = 9 and keep solving.


What should I do?

Thanks.
 
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  • #2
Just keep solving.
 
  • #3
Jimmy84 said:
What should I do?
Pick one and try it.

If you can't solve the problem, pick the other one.

If you can't solve the problem, go back to the first one (or try finding a third option).
 
  • #4
Mentallic said:
Just keep solving.

well the result on my book is - and + 1/2 square root of 3

If i keep solving I get 12x = +and- square root of 9 then x = +and- 3/ 12 then x = +and- 1/4 which is different.
 
  • #5
do this step by step

first take the 9 over which gives:

12x^2 = 9

then what would u do?
 
  • #6
sara_87 said:
do this step by step

first take the 9 over which gives:

12x^2 = 9

then what would u do?

I would move the square to the right, and I would have 12x = square root of nine isn't it?
 
  • #7
When you make an operation in solving equations, you need to perform the operation on both sides, but not only that, you need to perform squaring, square-rooting, etc. for every factor.

e.g. If we have [tex]x^2=a^2b[/tex] then to solve for x you're obviously going to take the square root of both sides. This gives us [tex]x=\sqrt{a^2b}[/tex] (lets ignore the [itex]\pm[/itex] for the moment) and if you use the property of square roots, you'll have [tex]x=\sqrt{a^2}\sqrt{b}[/tex] and simplifying, [tex]x=a\sqrt{b}[/tex]

Now look at your problem: You didn't follow the above for when you took the square root of [tex]12x^2[/tex].
 
  • #8
the ^2 only applies to the x

so remember it's 12 * x^2 = 9
 
  • #9
take the 12 to the other side
 
  • #10
sara_87 said:
the ^2 only applies to the x

so remember it's 12 * x^2 = 9

you are right x^2= 9/12 then x^2 = 3/4 and then to include the square root.
x = square root of 3/4

= 1/2 square root of 3 thanks a lot guys.. I appreciate it .
 
  • #11
There are two answers...
 

1. What does the equation 12x^2 - 9 = 0 mean?

The equation 12x^2 - 9 = 0 represents a quadratic equation, which is an equation with a degree of 2. It is in the form of ax^2 + bx + c = 0, where a, b, and c are coefficients and x is the variable.

2. How do I solve 12x^2 - 9 = 0?

To solve this equation, you can use the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 12, b = 0, and c = -9. Plugging these values into the formula, we get x = ±3/√3, which simplifies to x = ±√3.

3. What are the solutions to 12x^2 - 9 = 0?

The solutions to this equation are x = √3 and x = -√3. These are the values of x that make the equation true.

4. How do I check if my solutions are correct?

You can check your solutions by plugging them back into the original equation. For example, if x = √3, then 12(√3)^2 - 9 = 12(3) - 9 = 36 - 9 = 27, which is equal to 0. This confirms that √3 is a correct solution.

5. Are there any other methods to solve this equation?

Yes, there are other methods to solve quadratic equations such as factoring, completing the square, and graphing. However, the quadratic formula is the most commonly used method and can be applied to any quadratic equation.

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