Expert: Josh - 10/7/2008

Question
hey there would really appriciatie you taking the time to help me. the question states:3x^2-4=0 express your answer in simplest radical form. dont know if i should use the formula or complete the square as i am not good with factoring, also have another question how do i factor the following equation 3x^2-6.thank you very much

Answer
Hi Nabeel,

Generally speaking, we should use the quadratic formula
x=[-b+sqrt(b*b-4ac)]/(2a),[-b-sqrt(b*b-4ac)]/(2a)
only as our last resort.

with the 1st expression, the first step we should take is to separate the known "4" from the unknown "3x^2".

Adding 4 to both sides of the equation 3x^2-4=0, we have 3x^2=4.
Dividing both sides by 3, we get x^2=(4/3). Finally, taking the square root on both sides, we get x=2/sqrt(3) or -2/sqrt(3).

If we can spot a common factor in the expression, it's best to factorize it because the answer will soon become obvious.

e.g., with the second expression, 3x^2-6, notice that both terms (3x^2 and 6) are divisible by 3. So, we can pull the "3" out and treat it as a common factor. since 3x^2= 3*(x^2) and -6 = 3*(-2), we have 3x^2-6 = 3(x^2-2) that's how we factorize.

If you are asked to solve 3x^2-6=0, finding the solution to 3x^2-6=0 is equivalent to solving 3(x^2-2)=0. Using the square of difference result [x^2-a^2 = (x+a)(x-a), this holds for any real number a] we have 3(x+sqrt(2))(x-sqrt(2))=0

Remember that we are multiplying three terms on the left hand side (LHS). The LHS of the equation equals the RHS (zero)
if x+sqrt(2)=0, i.e., x=-sqrt(2) OR
if x-sqrt(2)=0, i.e., x=+sqrt(2).

So, the solutions are x=sqrt(2),-sqrt(2).

Another way to solve this is like the first example we've seen. First, separate the known from the unknown.
3x^2-6=0 becomes 3x^2=6.
Then, divide throughout by 3. We get x^2=2.
Finally, taking the square root on both sides, x=sqrt(2) or -sqrt(2).