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

[Jimmy84]

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.

 

[Mentallic]

Just keep solving.

 

[Hurkyl]

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).

 

[Jimmy84]

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.

 

[sara_87]

do this step by step

first take the 9 over which gives:

12x^2 = 9

then what would u do?

 

[Jimmy84]

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?

 

[Mentallic]

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

Now look at your problem: You didn't follow the above for when you took the square root of $$12x^2$$.

 

[sara_87]

the ^2 only applies to the x

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

 

[sara_87]

take the 12 to the other side

 

[Jimmy84]

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 .

 

[Mark44]

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