c^2+7c+12.25=0

Solution for c^2+7c+12.25=0 equation:

Simplifying
c2 + 7c + 12.25 = 0

Reorder the terms:
12.25 + 7c + c2 = 0

Solving
12.25 + 7c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '-12.25' to each side of the equation.
12.25 + 7c + -12.25 + c2 = 0 + -12.25

Reorder the terms:
12.25 + -12.25 + 7c + c2 = 0 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
0.00 + 7c + c2 = 0 + -12.25
7c + c2 = 0 + -12.25

Combine like terms: 0 + -12.25 = -12.25
7c + c2 = -12.25

The c term is 7c.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7c + 12.25 + c2 = -12.25 + 12.25

Reorder the terms:
12.25 + 7c + c2 = -12.25 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
12.25 + 7c + c2 = 0.00

Factor a perfect square on the left side:
(c + 3.5)(c + 3.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(c + 3.5) equal to 0.00 and 0.00.

Subproblem 1
c + 3.5 = 0.00

Simplifying
c + 3.5 = 0.00

Reorder the terms:
3.5 + c = 0.00

Solving
3.5 + c = 0.00

Solving for variable 'c'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + c = 0.00 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + c = 0.00 + -3.5
c = 0.00 + -3.5

Combine like terms: 0.00 + -3.5 = -3.5
c = -3.5

Simplifying
c = -3.5

Subproblem 2
c + 3.5 = 0.00

Simplifying
c + 3.5 = 0.00

Reorder the terms:
3.5 + c = 0.00

Solving
3.5 + c = 0.00

Solving for variable 'c'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + c = 0.00 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + c = 0.00 + -3.5
c = 0.00 + -3.5

Combine like terms: 0.00 + -3.5 = -3.5
c = -3.5

Simplifying
c = -3.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-3.5, -3.5}