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Simplifying
c2 + 3.75c + -1 = 0

Reorder the terms:
-1 + 3.75c + c2 = 0

Solving
-1 + 3.75c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3.75c + 1 + c2 = 0 + 1

Reorder the terms:
-1 + 1 + 3.75c + c2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3.75c + c2 = 0 + 1
3.75c + c2 = 0 + 1

Combine like terms: 0 + 1 = 1
3.75c + c2 = 1

The c term is 3.75c.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75c + 3.515625 + c2 = 1 + 3.515625

Reorder the terms:
3.515625 + 3.75c + c2 = 1 + 3.515625

Combine like terms: 1 + 3.515625 = 4.515625
3.515625 + 3.75c + c2 = 4.515625

Factor a perfect square on the left side:
(c + 1.875)(c + 1.875) = 4.515625

Calculate the square root of the right side: 2.125

Break this problem into two subproblems by setting 
(c + 1.875) equal to 2.125 and -2.125.

Subproblem 1

c + 1.875 = 2.125 Simplifying c + 1.875 = 2.125 Reorder the terms: 1.875 + c = 2.125 Solving 1.875 + c = 2.125 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + c = 2.125 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + c = 2.125 + -1.875 c = 2.125 + -1.875 Combine like terms: 2.125 + -1.875 = 0.25 c = 0.25 Simplifying c = 0.25

Subproblem 2

c + 1.875 = -2.125 Simplifying c + 1.875 = -2.125 Reorder the terms: 1.875 + c = -2.125 Solving 1.875 + c = -2.125 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + c = -2.125 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + c = -2.125 + -1.875 c = -2.125 + -1.875 Combine like terms: -2.125 + -1.875 = -4 c = -4 Simplifying c = -4

Solution

The solution to the problem is based on the solutions from the subproblems. c = {0.25, -4}
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