2c^2+3c-5=c+2

Solution for 2c^2+3c-5=c+2 equation:

Simplifying
2c2 + 3c + -5 = c + 2

Reorder the terms:
-5 + 3c + 2c2 = c + 2

Reorder the terms:
-5 + 3c + 2c2 = 2 + c

Solving
-5 + 3c + 2c2 = 2 + c

Solving for variable 'c'.

Reorder the terms:
-5 + -2 + 3c + -1c + 2c2 = 2 + c + -2 + -1c

Combine like terms: -5 + -2 = -7
-7 + 3c + -1c + 2c2 = 2 + c + -2 + -1c

Combine like terms: 3c + -1c = 2c
-7 + 2c + 2c2 = 2 + c + -2 + -1c

Reorder the terms:
-7 + 2c + 2c2 = 2 + -2 + c + -1c

Combine like terms: 2 + -2 = 0
-7 + 2c + 2c2 = 0 + c + -1c
-7 + 2c + 2c2 = c + -1c

Combine like terms: c + -1c = 0
-7 + 2c + 2c2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-3.5 + c + c2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + c + 3.5 + c2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + c + c2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + c + c2 = 0 + 3.5
c + c2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
c + c2 = 3.5

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.
 + 0.25 + c2 = 3.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + c2 = 3.5 + 0.25

Combine like terms: 3.5 + 0.25 = 3.75
1.25 + c2 = 3.75

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(c + 0.5) equal to 1.936491673 and -1.936491673.

Subproblem 1
c + 0.5 = 1.936491673

Simplifying
c + 0.5 = 1.936491673

Reorder the terms:
0.5 + c = 1.936491673

Solving
0.5 + c = 1.936491673

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 = 1.936491673 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = 1.936491673 + -0.5
c = 1.936491673 + -0.5

Combine like terms: 1.936491673 + -0.5 = 1.436491673
c = 1.436491673

Simplifying
c = 1.436491673

Subproblem 2
c + 0.5 = -1.936491673

Simplifying
c + 0.5 = -1.936491673

Reorder the terms:
0.5 + c = -1.936491673

Solving
0.5 + c = -1.936491673

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 = -1.936491673 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = -1.936491673 + -0.5
c = -1.936491673 + -0.5

Combine like terms: -1.936491673 + -0.5 = -2.436491673
c = -2.436491673

Simplifying
c = -2.436491673

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.436491673, -2.436491673}