PHY Electrostatics: PLEASEEE help! Determine the magnitude and direction of the resultant electric force on q

Four point charges are at the corners of a square of side a as shown in the figure below. Determine the magnitude and direction of the resultant electric force on q, with ke, q, and a left in symbolic form. (Let B = 2.5q and C = 6q. Let the +x-axis be pointing to the right.)

diagram: http://www.webassign.net/sercp9/15-p-008…

i went through and solved it, and got 19506 q/a as my magnitude, and 45 degrees as my direction. The magnitude was wrong, but the direction was correct.

can someone please help me out! i have been trying for so long and am stumped now :(

Coordinate system:
+x = right
+y = up

Define the leading constant, ke = 1/(4*pi*epsilon0) = 9*10^9 N-m^2/cou^2


Electric force from charge B:
Fbq = ke* Qb*q/a^2, in the direction to the right

As a vector:
Fbq = ke*q *


Electric force the other charge B (upward):
Fbbq = ke*q * <0, Qb/a^2>

Electric force from charge C (upward and rightward):

Total magnitude:
Fcq = ke*q*Qc/( sqrt(a^2 + a^2) )^2

sqrt(a^2 + a^2) = the hypotenuse distance
( sqrt(a^2 + a^2) )^2 = square it for Coulomb's law


Simplify:
Fcq = ke*q*Qc/(2*a^2)

Multiply with the up and to the right unit vector:
Fcq = ke*q*Qc/(2*a^2) *


Gather all the formulas for each individual force:
Fbq = ke*q *
Fbbq = ke*q * <0, Qb/a^2>
Fcq = ke*q*Qc/(2*a^2) *


Gather all common terms in the leading factor:
Fbq = ke*q/a^2 *
Fbbq = ke*q/a^2 * <0, Qb>
Fcq = ke*q/a^2 *

Add up the x-terms:
Qb + Qc*sqrt(2)/4

Add up the y-terms:
Qb + Qc*sqrt(2)/4

Compose the vector:
Fnet = Fbq + Fbbq + Fcq

Fnet = ke*q/a^2 *

Combine the vector components in Pythagorean theorem to find magnitude: