c^2-2c-30=0

Solution for c^2-2c-30=0 equation:

Simplifying
c2 + -2c + -30 = 0

Reorder the terms:
-30 + -2c + c2 = 0

Solving
-30 + -2c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -2c + 30 + c2 = 0 + 30

Reorder the terms:
-30 + 30 + -2c + c2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -2c + c2 = 0 + 30
-2c + c2 = 0 + 30

Combine like terms: 0 + 30 = 30
-2c + c2 = 30

The c term is -2c.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2c + 1 + c2 = 30 + 1

Reorder the terms:
1 + -2c + c2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + -2c + c2 = 31

Factor a perfect square on the left side:
(c + -1)(c + -1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(c + -1) equal to 5.567764363 and -5.567764363.

Subproblem 1
c + -1 = 5.567764363

Simplifying
c + -1 = 5.567764363

Reorder the terms:
-1 + c = 5.567764363

Solving
-1 + c = 5.567764363

Solving for variable 'c'.

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

Add '1' to each side of the equation.
-1 + 1 + c = 5.567764363 + 1

Combine like terms: -1 + 1 = 0
0 + c = 5.567764363 + 1
c = 5.567764363 + 1

Combine like terms: 5.567764363 + 1 = 6.567764363
c = 6.567764363

Simplifying
c = 6.567764363

Subproblem 2
c + -1 = -5.567764363

Simplifying
c + -1 = -5.567764363

Reorder the terms:
-1 + c = -5.567764363

Solving
-1 + c = -5.567764363

Solving for variable 'c'.

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

Add '1' to each side of the equation.
-1 + 1 + c = -5.567764363 + 1

Combine like terms: -1 + 1 = 0
0 + c = -5.567764363 + 1
c = -5.567764363 + 1

Combine like terms: -5.567764363 + 1 = -4.567764363
c = -4.567764363

Simplifying
c = -4.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {6.567764363, -4.567764363}