Solve for q:
16 = -5/(q (1-q))
16 = -5/((1-q) q) is equivalent to -5/((1-q) q) = 16:
-5/(q (1-q)) = 16
Take the reciprocal of both sides:
-1/5 q (1-q) = 1/16
Multiply both sides by -5:
q (1-q) = -5/16
Expand out terms of the left hand side:
q-q^2 = -5/16
Multiply both sides by -1:
q^2-q = 5/16
Add 1/4 to both sides:
q^2-q+1/4 = 9/16
Write the left hand side as a square:
(q-1/2)^2 = 9/16
Take the square root of both sides:
q-1/2 = 3/4 or q-1/2 = -3/4
Add 1/2 to both sides:
q = 5/4 or q-1/2 = -3/4
Add 1/2 to both sides:
Answer: |q = 5/4 or q = -1/4
