c^2+c-64=0

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Solution for c^2+c-64=0 equation: 


Simplifying
c2 + c + -64 = 0

Reorder the terms:
-64 + c + c2 = 0

Solving
-64 + c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + c + 64 + c2 = 0 + 64

Reorder the terms:
-64 + 64 + c + c2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + c + c2 = 0 + 64
c + c2 = 0 + 64

Combine like terms: 0 + 64 = 64
c + c2 = 64

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 = 64 + 0.25

Reorder the terms:
0.25 + c + c2 = 64 + 0.25

Combine like terms: 64 + 0.25 = 64.25
0.25 + c + c2 = 64.25

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(c + 0.5) equal to 8.015609771 and -8.015609771.


Subproblem 1
c + 0.5 = 8.015609771

Simplifying
c + 0.5 = 8.015609771

Reorder the terms:
0.5 + c = 8.015609771

Solving
0.5 + c = 8.015609771

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 = 8.015609771 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = 8.015609771 + -0.5
c = 8.015609771 + -0.5

Combine like terms: 8.015609771 + -0.5 = 7.515609771
c = 7.515609771

Simplifying
c = 7.515609771


Subproblem 2
c + 0.5 = -8.015609771

Simplifying
c + 0.5 = -8.015609771

Reorder the terms:
0.5 + c = -8.015609771

Solving
0.5 + c = -8.015609771

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 = -8.015609771 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = -8.015609771 + -0.5
c = -8.015609771 + -0.5

Combine like terms: -8.015609771 + -0.5 = -8.515609771
c = -8.515609771

Simplifying
c = -8.515609771


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {7.515609771, -8.515609771}

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