q(1-0.5q)=0.09499599

Solution for q(1-0.5q)=0.09499599 equation:

Simplifying
q(1 + -0.5q) = 0.09499599
(1 * q + -0.5q * q) = 0.09499599
(1q + -0.5q2) = 0.09499599

Solving
1q + -0.5q2 = 0.09499599

Solving for variable 'q'.

Reorder the terms:
-0.09499599 + 1q + -0.5q2 = 0.09499599 + -0.09499599

Combine like terms: 0.09499599 + -0.09499599 = 0.00000000
-0.09499599 + 1q + -0.5q2 = 0.00000000

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
0.18999198 + -2q + q2 = 0.0000000

Move the constant term to the right:

Add '-0.18999198' to each side of the equation.
0.18999198 + -2q + -0.18999198 + q2 = 0.0000000 + -0.18999198

Reorder the terms:
0.18999198 + -0.18999198 + -2q + q2 = 0.0000000 + -0.18999198

Combine like terms: 0.18999198 + -0.18999198 = 0.00000000
0.00000000 + -2q + q2 = 0.0000000 + -0.18999198
-2q + q2 = 0.0000000 + -0.18999198

Combine like terms: 0.0000000 + -0.18999198 = -0.18999198
-2q + q2 = -0.18999198

The q term is -2q.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2q + 1 + q2 = -0.18999198 + 1

Reorder the terms:
1 + -2q + q2 = -0.18999198 + 1

Combine like terms: -0.18999198 + 1 = 0.81000802
1 + -2q + q2 = 0.81000802

Factor a perfect square on the left side:
(q + -1)(q + -1) = 0.81000802

Calculate the square root of the right side: 0.900004456

Break this problem into two subproblems by setting 
(q + -1) equal to 0.900004456 and -0.900004456.

Subproblem 1
q + -1 = 0.900004456

Simplifying
q + -1 = 0.900004456

Reorder the terms:
-1 + q = 0.900004456

Solving
-1 + q = 0.900004456

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + q = 0.900004456 + 1

Combine like terms: -1 + 1 = 0
0 + q = 0.900004456 + 1
q = 0.900004456 + 1

Combine like terms: 0.900004456 + 1 = 1.900004456
q = 1.900004456

Simplifying
q = 1.900004456

Subproblem 2
q + -1 = -0.900004456

Simplifying
q + -1 = -0.900004456

Reorder the terms:
-1 + q = -0.900004456

Solving
-1 + q = -0.900004456

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + q = -0.900004456 + 1

Combine like terms: -1 + 1 = 0
0 + q = -0.900004456 + 1
q = -0.900004456 + 1

Combine like terms: -0.900004456 + 1 = 0.099995544
q = 0.099995544

Simplifying
q = 0.099995544

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {1.900004456, 0.099995544}