4x^2-9=0 i need help to solve this problem?

4x^2 = 9
x^2= 9/4
x= (9/4)^1/2
= + 3/2, - 3/2

since it is square root, so x has 2 values, which is + 3/2 and -3/2

Now, immediately by looking at the function, you already know that it is a quadratic function because it is of the degree 2.

This allows you to take 2 routes:
1.) By factoring (if possible)
2.) Quadratic Formula

Keep in mind, if route 1 is possible, it will take a lot less time to complete. Luckily, your function is factorable.

Through factoring, you get (2x+3)(2x-3) = 0

So now, you have to make the left side equal 0.
You can accomplish by making (2x+3) = 0
or by making (2x-3) = 0
As a result of simple algebra, you get x = 3/2 and x = -3/2.

You should get the same answer if you use the quadratic formula.

Hope this helps!

X-4 2 9

x² = 9/4

x = ± (3/2)

(2x-3)(2x+3)=0,
the rule here is a^2-b^2=(a-b)(a+b)
So, 2x-3=0 or 2x+3=0
therefore, 2x=3 or 2x=-3
hence, x=3/2 or x=-3/2
so the final answer is x=1.5 or x=-1.5 . pick whichever u like or need it both answers to the value of x is right. Now i explained to my best so might better choose me as the best answer.

4x^2=9
x^2=9/4
x=9/4^1/2

the square root of 9/4
reduce it 3/2
or 1 and 1/2

plug it in 4(1 1/2)^2-9=0

4(2 1/4)-9=0
9-9=0

4x^2-9=0
4x^2=9 (u bring the 9 to the otherside)
x^2=9/4 (u bring 4 to the other side)
x=+3/2 , -3/2 (square root of 9/4)

4x^2 = 9
x^2 = 9/4
x= + or - 3/2

4x^2 - 9 = 0
4x^2 = 9
x^2 = 9/4
x = ±√(9/4)
x = ±√[(3/2)^2]
x = ±3/2 (±1.5)

4x^2-9=(2x-3)(2x+3). (expand the right side and you will see that i am right) (you should memorize this way of factorizing polynomials) (this is called difference of squares)

anyway, since (2x-3)(2x+3)=0,
either 2x-3=0 OR 2x+3=0.

therefore, x=3/2 or -3/2.