I've been searching all over how to handle this issue I'm sitting with. Hope someone can help me out :)
I have to convert sentence (1) to (6) by removing the quadratic term in (1) with substitution (x = (t - a/3). I feel like I'm doing something wrong when calculation the squared parenthesis when there's a number in front of it as I'm suppose to remove the quadratic term? Can someone please take a look at the calculations and correct me if I'm wrong?
Thanks in advance!
The substitution $t-\frac a3$ is for a cubic equation of the form $x^3 + ax^2 + bx + c = 0.$
In order to make that formula apply to your particular equation, $x^3 + 1.5x^2 -2.5x + 2 = 0,$ all you need to do (and indeed what you must do) is to set $a=1.5,$ $b=-2.5,$ and $c=2.$
Having done that, you may (and in this case should) make the substitution $a = 1.5$ everywhere where the symbol $a$ occurs. If you do this, your $x^2$ terms will cancel.
You have a transcription error in the coefficient of your linear term, by the way; it was $-2.5$ initially but is later written $+2.5.$