c(c+1)=55

Solution for c(c+1)=55 equation:

Simplifying
c(c + 1) = 55

Reorder the terms:
c(1 + c) = 55
(1 * c + c * c) = 55
(1c + c2) = 55

Solving
1c + c2 = 55

Solving for variable 'c'.

Reorder the terms:
-55 + 1c + c2 = 55 + -55

Combine like terms: 55 + -55 = 0
-55 + 1c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '55' to each side of the equation.
-55 + 1c + 55 + c2 = 0 + 55

Reorder the terms:
-55 + 55 + 1c + c2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 1c + c2 = 0 + 55
1c + c2 = 0 + 55

Combine like terms: 0 + 55 = 55
1c + c2 = 55

The c term is 1c.  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 = 55 + 0.25

Reorder the terms:
0.25 + c + c2 = 55 + 0.25

Combine like terms: 55 + 0.25 = 55.25
0.25 + c + c2 = 55.25

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 55.25

Calculate the square root of the right side: 7.433034374

Break this problem into two subproblems by setting 
(c + 0.5) equal to 7.433034374 and -7.433034374.

Subproblem 1
c + 0.5 = 7.433034374

Simplifying
c + 0.5 = 7.433034374

Reorder the terms:
0.5 + c = 7.433034374

Solving
0.5 + c = 7.433034374

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 = 7.433034374 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = 7.433034374 + -0.5
c = 7.433034374 + -0.5

Combine like terms: 7.433034374 + -0.5 = 6.933034374
c = 6.933034374

Simplifying
c = 6.933034374

Subproblem 2
c + 0.5 = -7.433034374

Simplifying
c + 0.5 = -7.433034374

Reorder the terms:
0.5 + c = -7.433034374

Solving
0.5 + c = -7.433034374

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 = -7.433034374 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = -7.433034374 + -0.5
c = -7.433034374 + -0.5

Combine like terms: -7.433034374 + -0.5 = -7.933034374
c = -7.933034374

Simplifying
c = -7.933034374

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {6.933034374, -7.933034374}