Help factoring what seems to be a simple quadratic..?

Question

Please help me solve this by factoring..

2x^2 + 3x - 2 = 0

I don't know why I'm having such a hard time with it.

Answer 1

Determine the factors of the first term 2x^2, which would be :

2x and x

Determine the factors of the last term - 2, which would be :

-2 and 1
or
2 and -1

The middle term would tell us which should be combined. And it should be the sum of the inner and outer products of our factors.

(2x - 2) (x + 1)
if we get the sum of the inner and outer products(-2x) + (2x), it will give us 0. So, this is not the right combinations. Let's try the other one :

(2x - 1) (x + 2)
the sum of the inner and outer products -x + 4x = +3x.
Therefore, the factors of the given quadratic equation is :

(2x - 1) (x + 2)

Answer 2

I hope this helps. Have your teacher tought you the X method. If yes this helps if not try your best to understand.
If you know that the 2x^2 is the A, the 3X is the B and finally the -2 is the C.
First by making an X near (not so far away) from the equation. Make sure it's bigger the multiplication symbol.

As you look at the X you realize there is four empty spaces.
After realizing that Multiply the A and C. It should be -4. That goes on top space in X.

For the B (3x) waht goes on the bottom of X is 3.

After doing that realizing that there is blanks on the X left and right. What you must do is find a product that matches AC combined. Also what goes into the sum of 3 from B. I got -4 and 1. Try it out if your not sure.

Second place the equation out like this:
2x^2-4X+1X-2=0
Circle 2x^2-4X and 1X-2
Then distribute these set ups like this
2X(X-2)+1(X-2)

Third write down the two equations
2x+1=0 and X-2+0
After that simplify
If that is successful you should get two answers
X=1/2 and X=2

Sorry if this was confusing in any way. Doing Algebra or Algebra 2 can be tricky I went through it too.

Answer 3

(x + 2)(x - 3) = 20 x^2 - x - 6 = 20 x^2 - x = 26 finished the sq." x^2 - x + a million/4 = 26 + a million/4 (x - a million/2)^2 = 104/4 + a million/4 = a hundred and five/4 x - a million/2 = ±?(a hundred and five/4) x = a million/2(a million + ?a hundred and five) x = a million/2(a million - ?a hundred and five)

Answer 4

(2x-1)(x+2)=0