You are restricted from using any other approach besides completing squares
F(x)=6x2-60x+126.
To complete the square for this equation, we will focus on the x^2 and x terms.
1. Start by factoring out the coefficient of x^2 which is 6:
F(x) = 6(x^2 - 10x) + 126
2. To complete the square for the expression in the parentheses, we take half of the coefficient of x (-10) and square it:
(-10/2)^2 = (-5)^2 = 25
3. Add and subtract this value inside the parentheses:
F(x) = 6(x^2 - 10x + 25 - 25) + 126
4. Simplify:
F(x) = 6((x - 5)^2 - 25) + 126
F(x) = 6(x - 5)^2 - 150 + 126
F(x) = 6(x - 5)^2 - 24
Therefore, the completed square form of the function F(x) = 6x^2 - 60x + 126 is F(x) = 6(x - 5)^2 - 24.