To complete the square, begin by grouping the `x^2` and `x` terms:
Now factor out the `-3`
The formula you need now is `(b/2)^2` .
In this case, that is `(-2/2)^2` which equals `1` .
You must both add and subtract it from the problem, so as not to change its value.
The trick is that `1` which is added inside the parentheses is being multiplied by a distributed `-3` . Therefore, you are not really adding `1` , you are subtracting `3` . To counteract that, you must add `3` on the outside.
Then you must change the part inside the parentheses to a perfect square. Take the square root of the first and last terms, and use the sign from the middle term.
-3x^2 + 6x -4 = -3x^2 + 6x - 3 -1 = -3 (x^2 -2x +1) -1 = -3(x-1)^2 -1 . same as the books answer.
remember, (x-1)^2 = x^2-2x+1