c^2-9c-32=0

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Solution for c^2-9c-32=0 equation: 


Simplifying
c2 + -9c + -32 = 0

Reorder the terms:
-32 + -9c + c2 = 0

Solving
-32 + -9c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -9c + 32 + c2 = 0 + 32

Reorder the terms:
-32 + 32 + -9c + c2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -9c + c2 = 0 + 32
-9c + c2 = 0 + 32

Combine like terms: 0 + 32 = 32
-9c + c2 = 32

The c term is -9c.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9c + 20.25 + c2 = 32 + 20.25

Reorder the terms:
20.25 + -9c + c2 = 32 + 20.25

Combine like terms: 32 + 20.25 = 52.25
20.25 + -9c + c2 = 52.25

Factor a perfect square on the left side:
(c + -4.5)(c + -4.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(c + -4.5) equal to 7.228416147 and -7.228416147.


Subproblem 1
c + -4.5 = 7.228416147

Simplifying
c + -4.5 = 7.228416147

Reorder the terms:
-4.5 + c = 7.228416147

Solving
-4.5 + c = 7.228416147

Solving for variable 'c'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + c = 7.228416147 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + c = 7.228416147 + 4.5
c = 7.228416147 + 4.5

Combine like terms: 7.228416147 + 4.5 = 11.728416147
c = 11.728416147

Simplifying
c = 11.728416147


Subproblem 2
c + -4.5 = -7.228416147

Simplifying
c + -4.5 = -7.228416147

Reorder the terms:
-4.5 + c = -7.228416147

Solving
-4.5 + c = -7.228416147

Solving for variable 'c'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + c = -7.228416147 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + c = -7.228416147 + 4.5
c = -7.228416147 + 4.5

Combine like terms: -7.228416147 + 4.5 = -2.728416147
c = -2.728416147

Simplifying
c = -2.728416147


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {11.728416147, -2.728416147}

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