find the magnitude and direction needed to accelerate a 100-g mass with an acceleration = -.255 m/s squared+.650 m/s squared

If a single force is used:

a = -255 + 650 = 395 m/s^2
F = m * a = 0.1 * 395 = 39.5 N. Along the +x axis.

If 2 forces are used:
F1 = 0.1 * (-255 = -25.5 N. Along the -x
axis.
F2 = 0.1 * 650 = 65 N. Along the +x axis.
Fn = -25.5 + 65 = 39.5 N. = Net force
Acting along the +x axis.