q^2+2q-41=0

Solution for q^2+2q-41=0 equation:

Simplifying
q2 + 2q + -41 = 0

Reorder the terms:
-41 + 2q + q2 = 0

Solving
-41 + 2q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 2q + 41 + q2 = 0 + 41

Reorder the terms:
-41 + 41 + 2q + q2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 2q + q2 = 0 + 41
2q + q2 = 0 + 41

Combine like terms: 0 + 41 = 41
2q + q2 = 41

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 = 41 + 1

Reorder the terms:
1 + 2q + q2 = 41 + 1

Combine like terms: 41 + 1 = 42
1 + 2q + q2 = 42

Factor a perfect square on the left side:
(q + 1)(q + 1) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(q + 1) equal to 6.480740698 and -6.480740698.

Subproblem 1
q + 1 = 6.480740698

Simplifying
q + 1 = 6.480740698

Reorder the terms:
1 + q = 6.480740698

Solving
1 + q = 6.480740698

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 = 6.480740698 + -1

Combine like terms: 1 + -1 = 0
0 + q = 6.480740698 + -1
q = 6.480740698 + -1

Combine like terms: 6.480740698 + -1 = 5.480740698
q = 5.480740698

Simplifying
q = 5.480740698

Subproblem 2
q + 1 = -6.480740698

Simplifying
q + 1 = -6.480740698

Reorder the terms:
1 + q = -6.480740698

Solving
1 + q = -6.480740698

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 = -6.480740698 + -1

Combine like terms: 1 + -1 = 0
0 + q = -6.480740698 + -1
q = -6.480740698 + -1

Combine like terms: -6.480740698 + -1 = -7.480740698
q = -7.480740698

Simplifying
q = -7.480740698

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {5.480740698, -7.480740698}