Answer:
9 - 2(x+1.5)²
Step-by-step explanation:
To solve this, we can apply a process called "Completing the Square". To do this, we can first separate the 9 and add that back later, leaving us with
-6x-2x² = -2x²-6x
Then, we can factor out the number that attaches to the x² (its coefficient, which is -2 in this case) to get
-2 (x²+3x)
After that, we can divide the coefficient of the x by 2, so 3/2 = 1.5 in this case, and representing that as q, we can write our expression as
-2 (x+q)². Plugging 1.5 in for q in this case, we get
-2(x+1.5)²
Now, we need to reconcile this with our original expression of
9-6x-2x². To do this, we can first expand -2(x+1.5)² to get
-2(x²+3x+2.25) = -2x²-6x-4.5. We now have
-2x²-6x-4.5 and want to turn it into
9-6x-2x² = -2x²-6x+9
To do this, we can add 13.5 to -2x²-6x-4.5, so our expression is
-2x²-6x-4.5 + 13.5
= -2(x+1.5)² + 9
= 9 - 2(x+1.5)²
