c^2+c+41=67

Solution for c^2+c+41=67 equation:

Simplifying
c2 + c + 41 = 67

Reorder the terms:
41 + c + c2 = 67

Solving
41 + c + c2 = 67

Solving for variable 'c'.

Reorder the terms:
41 + -67 + c + c2 = 67 + -67

Combine like terms: 41 + -67 = -26
-26 + c + c2 = 67 + -67

Combine like terms: 67 + -67 = 0
-26 + c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + c + 26 + c2 = 0 + 26

Reorder the terms:
-26 + 26 + c + c2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + c + c2 = 0 + 26
c + c2 = 0 + 26

Combine like terms: 0 + 26 = 26
c + c2 = 26

The c term is c.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
c + 0.25 + c2 = 26 + 0.25

Reorder the terms:
0.25 + c + c2 = 26 + 0.25

Combine like terms: 26 + 0.25 = 26.25
0.25 + c + c2 = 26.25

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(c + 0.5) equal to 5.123475383 and -5.123475383.

Subproblem 1
c + 0.5 = 5.123475383

Simplifying
c + 0.5 = 5.123475383

Reorder the terms:
0.5 + c = 5.123475383

Solving
0.5 + c = 5.123475383

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = 5.123475383 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = 5.123475383 + -0.5
c = 5.123475383 + -0.5

Combine like terms: 5.123475383 + -0.5 = 4.623475383
c = 4.623475383

Simplifying
c = 4.623475383

Subproblem 2
c + 0.5 = -5.123475383

Simplifying
c + 0.5 = -5.123475383

Reorder the terms:
0.5 + c = -5.123475383

Solving
0.5 + c = -5.123475383

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = -5.123475383 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = -5.123475383 + -0.5
c = -5.123475383 + -0.5

Combine like terms: -5.123475383 + -0.5 = -5.623475383
c = -5.623475383

Simplifying
c = -5.623475383

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {4.623475383, -5.623475383}