c^2+5c-15=0

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Solution for c^2+5c-15=0 equation: 


Simplifying
c2 + 5c + -15 = 0

Reorder the terms:
-15 + 5c + c2 = 0

Solving
-15 + 5c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 5c + 15 + c2 = 0 + 15

Reorder the terms:
-15 + 15 + 5c + c2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 5c + c2 = 0 + 15
5c + c2 = 0 + 15

Combine like terms: 0 + 15 = 15
5c + c2 = 15

The c term is 5c.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5c + 6.25 + c2 = 15 + 6.25

Reorder the terms:
6.25 + 5c + c2 = 15 + 6.25

Combine like terms: 15 + 6.25 = 21.25
6.25 + 5c + c2 = 21.25

Factor a perfect square on the left side:
(c + 2.5)(c + 2.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(c + 2.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
c + 2.5 = 4.609772229

Simplifying
c + 2.5 = 4.609772229

Reorder the terms:
2.5 + c = 4.609772229

Solving
2.5 + c = 4.609772229

Solving for variable 'c'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + c = 4.609772229 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = 4.609772229 + -2.5
c = 4.609772229 + -2.5

Combine like terms: 4.609772229 + -2.5 = 2.109772229
c = 2.109772229

Simplifying
c = 2.109772229


Subproblem 2
c + 2.5 = -4.609772229

Simplifying
c + 2.5 = -4.609772229

Reorder the terms:
2.5 + c = -4.609772229

Solving
2.5 + c = -4.609772229

Solving for variable 'c'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + c = -4.609772229 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = -4.609772229 + -2.5
c = -4.609772229 + -2.5

Combine like terms: -4.609772229 + -2.5 = -7.109772229
c = -7.109772229

Simplifying
c = -7.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {2.109772229, -7.109772229}

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