(5c^2)=31c-28

Solution for (5c^2)=31c-28 equation:

Simplifying
(5c2) = 31c + -28

Reorder the terms:
(5c2) = -28 + 31c

Solving
(5c2) = -28 + 31c

Solving for variable 'c'.

Reorder the terms:
28 + -31c + (5c2) = -28 + 31c + 28 + -31c

Reorder the terms:
28 + -31c + (5c2) = -28 + 28 + 31c + -31c

Combine like terms: -28 + 28 = 0
28 + -31c + (5c2) = 0 + 31c + -31c
28 + -31c + (5c2) = 31c + -31c

Combine like terms: 31c + -31c = 0
28 + -31c + (5c2) = 0

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

Divide each side by '5'.
5.6 + -6.2c + c2 = 0

Move the constant term to the right:

Add '-5.6' to each side of the equation.
5.6 + -6.2c + -5.6 + c2 = 0 + -5.6

Reorder the terms:
5.6 + -5.6 + -6.2c + c2 = 0 + -5.6

Combine like terms: 5.6 + -5.6 = 0.0
0.0 + -6.2c + c2 = 0 + -5.6
-6.2c + c2 = 0 + -5.6

Combine like terms: 0 + -5.6 = -5.6
-6.2c + c2 = -5.6

The c term is -6.2c.  Take half its coefficient (-3.1).
Square it (9.61) and add it to both sides.

Add '9.61' to each side of the equation.
-6.2c + 9.61 + c2 = -5.6 + 9.61

Reorder the terms:
9.61 + -6.2c + c2 = -5.6 + 9.61

Combine like terms: -5.6 + 9.61 = 4.01
9.61 + -6.2c + c2 = 4.01

Factor a perfect square on the left side:
((c) + -3.1)((c) + -3.1) = 4.01

Calculate the square root of the right side: 2.002498439

Break this problem into two subproblems by setting 
((c) + -3.1) equal to 2.002498439 and -2.002498439.

Subproblem 1
(c) + -3.1 = 2.002498439

Simplifying
(c) + -3.1 = 2.002498439
c + -3.1 = 2.002498439

Reorder the terms:
-3.1 + c = 2.002498439

Solving
-3.1 + c = 2.002498439

Solving for variable 'c'.

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

Add '3.1' to each side of the equation.
-3.1 + 3.1 + c = 2.002498439 + 3.1

Combine like terms: -3.1 + 3.1 = 0.0
0.0 + c = 2.002498439 + 3.1
c = 2.002498439 + 3.1

Combine like terms: 2.002498439 + 3.1 = 5.102498439
c = 5.102498439

Simplifying
c = 5.102498439

Subproblem 2
(c) + -3.1 = -2.002498439

Simplifying
(c) + -3.1 = -2.002498439
c + -3.1 = -2.002498439

Reorder the terms:
-3.1 + c = -2.002498439

Solving
-3.1 + c = -2.002498439

Solving for variable 'c'.

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

Add '3.1' to each side of the equation.
-3.1 + 3.1 + c = -2.002498439 + 3.1

Combine like terms: -3.1 + 3.1 = 0.0
0.0 + c = -2.002498439 + 3.1
c = -2.002498439 + 3.1

Combine like terms: -2.002498439 + 3.1 = 1.097501561
c = 1.097501561

Simplifying
c = 1.097501561

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {5.102498439, 1.097501561}