q^2+2q-27=0

Solution for q^2+2q-27=0 equation:

Simplifying
q2 + 2q + -27 = 0

Reorder the terms:
-27 + 2q + q2 = 0

Solving
-27 + 2q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 2q + 27 + q2 = 0 + 27

Reorder the terms:
-27 + 27 + 2q + q2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 2q + q2 = 0 + 27
2q + q2 = 0 + 27

Combine like terms: 0 + 27 = 27
2q + q2 = 27

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 = 27 + 1

Reorder the terms:
1 + 2q + q2 = 27 + 1

Combine like terms: 27 + 1 = 28
1 + 2q + q2 = 28

Factor a perfect square on the left side:
(q + 1)(q + 1) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(q + 1) equal to 5.291502622 and -5.291502622.

Subproblem 1
q + 1 = 5.291502622

Simplifying
q + 1 = 5.291502622

Reorder the terms:
1 + q = 5.291502622

Solving
1 + q = 5.291502622

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 = 5.291502622 + -1

Combine like terms: 1 + -1 = 0
0 + q = 5.291502622 + -1
q = 5.291502622 + -1

Combine like terms: 5.291502622 + -1 = 4.291502622
q = 4.291502622

Simplifying
q = 4.291502622

Subproblem 2
q + 1 = -5.291502622

Simplifying
q + 1 = -5.291502622

Reorder the terms:
1 + q = -5.291502622

Solving
1 + q = -5.291502622

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 = -5.291502622 + -1

Combine like terms: 1 + -1 = 0
0 + q = -5.291502622 + -1
q = -5.291502622 + -1

Combine like terms: -5.291502622 + -1 = -6.291502622
q = -6.291502622

Simplifying
q = -6.291502622

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {4.291502622, -6.291502622}