c^2-3c=-1

Solution for c^2-3c=-1 equation:

Simplifying
c2 + -3c = -1

Reorder the terms:
-3c + c2 = -1

Solving
-3c + c2 = -1

Solving for variable 'c'.

Reorder the terms:
1 + -3c + c2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -3c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3c + -1 + c2 = 0 + -1

Reorder the terms:
1 + -1 + -3c + c2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3c + c2 = 0 + -1
-3c + c2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3c + c2 = -1

The c term is -3c.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3c + 2.25 + c2 = -1 + 2.25

Reorder the terms:
2.25 + -3c + c2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3c + c2 = 1.25

Factor a perfect square on the left side:
(c + -1.5)(c + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(c + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
c + -1.5 = 1.118033989

Simplifying
c + -1.5 = 1.118033989

Reorder the terms:
-1.5 + c = 1.118033989

Solving
-1.5 + c = 1.118033989

Solving for variable 'c'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + c = 1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + c = 1.118033989 + 1.5
c = 1.118033989 + 1.5

Combine like terms: 1.118033989 + 1.5 = 2.618033989
c = 2.618033989

Simplifying
c = 2.618033989

Subproblem 2
c + -1.5 = -1.118033989

Simplifying
c + -1.5 = -1.118033989

Reorder the terms:
-1.5 + c = -1.118033989

Solving
-1.5 + c = -1.118033989

Solving for variable 'c'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + c = -1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + c = -1.118033989 + 1.5
c = -1.118033989 + 1.5

Combine like terms: -1.118033989 + 1.5 = 0.381966011
c = 0.381966011

Simplifying
c = 0.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {2.618033989, 0.381966011}