How would i solve this? 9x^2-4=0?? plz make it simple?

Question

Here are the answer choices : A: -4/9,4/9. B: -2/3,2/3. C: -3/2.3/2 and D:-9/4.9/4. i dont want the answer, i just want to know how to solve it. i posted the answers so you will get the whole picture. if you can plz make it simple to understand

Answer 1

Here it goes:

9x^2=4.
x^2=(4/9).

Take sqrt of both sides....

x= +/- 2/3.

Your answer is B!

Answer 2

First, add 4 to both sides giving you 9x^2=4. Then divide both sides by 9 to get x^2=9/4. Then take the square root of both sides to get x=3/2 or x=-3/2.

Answer 3

The whole problem is to get the x by itself on one side of the equal sign. Work in order from simple sign to the more complex (+/- first, then multiply/divide, then do exponents). So start by adding 4 to both sides:
9x^2-4+4 = 0+4 . . . 9x^2=4

Next, divide both sides by 9:
9x^2/9 = 4/9 . . . x^2=4/9

Finally, take the square root of both sides:
sqrt(x^2) = sqrt(4/9) . . . x=2/3, -2/3

You can get this - just remember the order of operations. Do what you need to in order to get the x by itself - that's the whole point of the problem.

Answer 4

you add 4 to both sides so you get 9x^2 = 4. Then you divide both sides by 9 to get x^2 = 4/9. Then you take the square root of both sides, so you get two possible answers because a negative times a negative is a positive, but so is a positive times a positive (when you square the answers, they are both positive). So you get 2/3 and -2/3.

Answer 5

9x^2 - 4 = 0

Get all the "x's" on one side and the numbers on the other:

9x^2 - 4 = 0
9x^2 - 4 + 4 = 0 + 4
9x^2 + 0 = 4
9x^2 = 4


Now, divide both sides by 9:

(9x^2)/9 = 4/9
(9/9)x^2 = 4/9
1*x^2 = 4/9
x^2 = 4/9

Take square roots of both sides, but remember when you take a square root of say, "4", the answer will be "+2, -2"

sqrt(x^2) = sqrt(4/9)
x = sqrt(4) / sqrt(9)
x = +/- 2/3
x = +2/3 or -2/3

Answer 6

The KEY to solving algebra problems is to get the unknown variable (X in this case) all by itself on 1 side of the equal sign by doing the exact OPPOSITE of what's being done right now.

With 9X^2 - 4 = 0, you're:

1) Subracting 4. To undo this, you'd add 4 to both sides, which would leave you with 9X^2 = 4.

2) Multiply by 9, so we'd undo this by dividing both sides by 9, leaving you with X^2 = 4/9.

3) Multiplying X by itself (squaring X). To undo this, we'd take the square root of both sides, leaving us with X = sqr root (4/9) = 2/3 or - 2/3. So choice B would be the right one.

Answer 7

both those terms are perfect squares, and if you have the difference of two squares, the correct factorization goes as follows:

a^2 - b^2 = (a + b)(a - b)

in your case, a^2 = 9x^2, so a = sqrt(9x^2) = 3x (unsquare each factor). b^2 = 4, b = 2.

so, the factorization is (3x + 2)(3x - 2).

so, since this must be equal to zero, x = 2/3 or -2/3.

note: if you take either a or b or both to be their negatives (where a = -3x or b = -2) you still arrive at an equivalent factorization. try it!

:)

Answer 8

Hi,

when trying to solve for a variable...you're trying to isolate it...so:

step1: add 4 to both sides of the equation...giving u:

9x^2-4 +4 = 4

simplifying you get:

9x^2 = 4

step 2: divide both sides by 9 and you have:

x^2 = 4/9

step 3: now take the square root of both sides:

and you should get your answer. (square root of 4 over the square root of 9)

hope that helps!

Answer 9

This is a difference of two squares.

Use the formula to get your answer: [F]^2 - [L]^2 = (F + L) (F - L).

First, you have to find F. In ordered to find F, you need to ask yourself what number can give you 9x^2 if you square it.
The answer is F = 3x.

Next, you have to find L. In ordered to find L, you need to ask yourself what number can give you 4^2 if you square it.
The answer is L = 2.

Then, you go back to the formula:
[F]^2 - [L]^2 = [3x]^2 - [2]^2 = (3x + 2) (3x - 2).

After that, you solve both of the equations by setting them equal to zero:

3x +2 = 0 x = -2/3
3x - 2 = 0 x = 2/3

So, the answer would be B.

Answer 10

9x^2-4 = 0
9x^2 = 4
x^2 = 4/9
x = sqrt of 4/9
= +2/3 or -2/3