12 3 4 5 6 7 8 9 10 time remaining 48: 54 what number should be added to both sides of the equation to complete the square? x2 + 3x = 6 3 62

2.25

Consider the square ...

... (x+a)² = x² +2ax +a²

The constant term (a²) is the square of half the x-coefficient: a² = (2a/2)².

The x-coefficient in your expression is 3. The square of half that is ...

... (3/2)² = 9/4 = 2.25

Adding 2.25 to both sides gives ...

... x² +3x + 2.25 = 6 + 2.25

... (x +1.5)² = 8.25 . . . . completed square

(3/2)^2

I believe it is (3/2)^2 because I tried working it out and got something like it. I did get an answer of x = ± over 2.

Most sources appear to give 2.25, which is equal to 3/2 squared.

Attached some work.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50