C^2-24C+10=0

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Solution for C^2-24C+10=0 equation: 


Simplifying
C2 + -24C + 10 = 0

Reorder the terms:
10 + -24C + C2 = 0

Solving
10 + -24C + C2 = 0

Solving for variable 'C'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -24C + -10 + C2 = 0 + -10

Reorder the terms:
10 + -10 + -24C + C2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -24C + C2 = 0 + -10
-24C + C2 = 0 + -10

Combine like terms: 0 + -10 = -10
-24C + C2 = -10

The C term is -24C.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24C + 144 + C2 = -10 + 144

Reorder the terms:
144 + -24C + C2 = -10 + 144

Combine like terms: -10 + 144 = 134
144 + -24C + C2 = 134

Factor a perfect square on the left side:
(C + -12)(C + -12) = 134

Calculate the square root of the right side: 11.575836903

Break this problem into two subproblems by setting 
(C + -12) equal to 11.575836903 and -11.575836903.


Subproblem 1
C + -12 = 11.575836903

Simplifying
C + -12 = 11.575836903

Reorder the terms:
-12 + C = 11.575836903

Solving
-12 + C = 11.575836903

Solving for variable 'C'.

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

Add '12' to each side of the equation.
-12 + 12 + C = 11.575836903 + 12

Combine like terms: -12 + 12 = 0
0 + C = 11.575836903 + 12
C = 11.575836903 + 12

Combine like terms: 11.575836903 + 12 = 23.575836903
C = 23.575836903

Simplifying
C = 23.575836903


Subproblem 2
C + -12 = -11.575836903

Simplifying
C + -12 = -11.575836903

Reorder the terms:
-12 + C = -11.575836903

Solving
-12 + C = -11.575836903

Solving for variable 'C'.

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

Add '12' to each side of the equation.
-12 + 12 + C = -11.575836903 + 12

Combine like terms: -12 + 12 = 0
0 + C = -11.575836903 + 12
C = -11.575836903 + 12

Combine like terms: -11.575836903 + 12 = 0.424163097
C = 0.424163097

Simplifying
C = 0.424163097


Solution
The solution to the problem is based on the solutions
from the subproblems.
C = {23.575836903, 0.424163097}

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