Rewrite the expression 6j^2 - 6j - 12 in the form c(j + p)^2 + q, where c, p, and q are constants. What is q/p?
+2668 The equation can be written as \(6(j^2-j-2)\).
We can divide the equation by \(6\) to get \(j^2-j-2\).
This is: \(j^2-j-2=0\)
Add \(2\) to both sides: \(j^2-j=2\)
Rewrite: \((j-0.5)^2 = 2+0.25\)
So: \(6(j-0.5)^2 = 6j^2-6j+1.5\)
We need to subtract \(13\) to get the equation, so we have: \(6(j-0.5)^2-13\)
Thus, the answer is \({-13\over-0.5} = \color{brown}\boxed{26}\)
