You could simplify this work by factoring "3" out of all four terms, as follows:
3(x^2 + 2x - 3) =3(0) = 0
Hold the 3 for later re-insertion. Focus on "completing the square" of x^2 + 2x - 3.
1. Take the coefficient (2) of x and halve it: 2 divided by 2 is 1 2. Square this result: 1^2 = 1 3. Add this result (1) to x^2 + 2x, holding the "-3" for later: x^2 +2x 4 Subtract (1) from x^2 + 2x + 1: x^2 + 2x + 1 -3 -1 = 0, or x^2 + 2x + 1 - 4 = 0 5. Simplify, remembering that x^2 + 2x + 1 is a perfect square:
(x+1)^2 - 4 = 0
We have "completed the square." We can stop here. or, we could solve for x: one way would be to factor the left side:
[(x+1)-2][(x+1)+2]=0 The solutions would then be:
x+1-2=0=> x-1=0, or x=1, and x+1 +2 = 0 => x+3=0, or x=-3. (you were not asked to do this).
