2-q^2=8+2q

Solution for 2-q^2=8+2q equation:

Simplifying
2 + -1q2 = 8 + 2q

Solving
2 + -1q2 = 8 + 2q

Solving for variable 'q'.

Reorder the terms:
2 + -8 + -2q + -1q2 = 8 + 2q + -8 + -2q

Combine like terms: 2 + -8 = -6
-6 + -2q + -1q2 = 8 + 2q + -8 + -2q

Reorder the terms:
-6 + -2q + -1q2 = 8 + -8 + 2q + -2q

Combine like terms: 8 + -8 = 0
-6 + -2q + -1q2 = 0 + 2q + -2q
-6 + -2q + -1q2 = 2q + -2q

Combine like terms: 2q + -2q = 0
-6 + -2q + -1q2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 2q + q2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 2q + q2)' equal to zero and attempt to solve:

Simplifying
6 + 2q + q2 = 0

Solving
6 + 2q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 2q + -6 + q2 = 0 + -6

Reorder the terms:
6 + -6 + 2q + q2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 2q + q2 = 0 + -6
2q + q2 = 0 + -6

Combine like terms: 0 + -6 = -6
2q + q2 = -6

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 = -6 + 1

Reorder the terms:
1 + 2q + q2 = -6 + 1

Combine like terms: -6 + 1 = -5
1 + 2q + q2 = -5

Factor a perfect square on the left side:
(q + 1)(q + 1) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.