c+c*c=0.24

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Solution for c+c*c=0.24 equation: 


Simplifying
c + c * c = 0.24

Multiply c * c
c + c2 = 0.24

Solving
c + c2 = 0.24

Solving for variable 'c'.

Reorder the terms:
-0.24 + c + c2 = 0.24 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
-0.24 + c + c2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.24' to each side of the equation.
-0.24 + c + 0.24 + c2 = 0.00 + 0.24

Reorder the terms:
-0.24 + 0.24 + c + c2 = 0.00 + 0.24

Combine like terms: -0.24 + 0.24 = 0.00
0.00 + c + c2 = 0.00 + 0.24
c + c2 = 0.00 + 0.24

Combine like terms: 0.00 + 0.24 = 0.24
c + c2 = 0.24

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.
c + 0.25 + c2 = 0.24 + 0.25

Reorder the terms:
0.25 + c + c2 = 0.24 + 0.25

Combine like terms: 0.24 + 0.25 = 0.49
0.25 + c + c2 = 0.49

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 0.49

Calculate the square root of the right side: 0.7

Break this problem into two subproblems by setting 
(c + 0.5) equal to 0.7 and -0.7.


Subproblem 1
c + 0.5 = 0.7

Simplifying
c + 0.5 = 0.7

Reorder the terms:
0.5 + c = 0.7

Solving
0.5 + c = 0.7

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 = 0.7 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = 0.7 + -0.5
c = 0.7 + -0.5

Combine like terms: 0.7 + -0.5 = 0.2
c = 0.2

Simplifying
c = 0.2


Subproblem 2
c + 0.5 = -0.7

Simplifying
c + 0.5 = -0.7

Reorder the terms:
0.5 + c = -0.7

Solving
0.5 + c = -0.7

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 = -0.7 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = -0.7 + -0.5
c = -0.7 + -0.5

Combine like terms: -0.7 + -0.5 = -1.2
c = -1.2

Simplifying
c = -1.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.2, -1.2}

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