00:01
For number 34, we're going to be going over solving a quadratic equation using the complete the square method.
00:07
So for number 34, we're given the quadratic equation 3x squared minus 2x minus 4 equals 0.
00:17
So we need to solve this using the complete the square method.
00:20
So the first step is we need to get a binomial on its own.
00:24
We need a binomial isolated on one side.
00:27
And we need that binomial to be in the form of x squared plus b.
00:31
First step is going to move this card constant 4 over.
00:35
So we'll add 4 to both sides.
00:36
We'll get 3x squared minus 2x equals 4.
00:41
Next we need to get rid of the coefficient on our x squared.
00:45
So we're going to divide both sides by 3.
00:47
We'll get x squared minus 2 thirds x equals 4 thirds.
00:54
So now that we have our binomial on its own in x squared plus bx form, we can find our b over 2 squared and this is what we're going to be adding to both sides and on the left it'll give us a perfect square trigonial that we can simplify out that we can factor and then square with both sides so for x so a b in this case is going to be minus two -thirds so we will have minus two -thirds two -thirds over two squared a few too many lines there there we go so we can simplify this out so two -thirds over is going to be minus two -sixths, which is going to be minus one -third squared, and minus one -third squared is going to be one -ninth.
01:51
So now we have our b over two squared.
01:54
We can plug that into both sides.
01:56
So on the left, we'll have our perfect square trinomial, x squared minus two -thirds x plus one -ninth...