0.5(c-8)(c-8)=3

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Solution for 0.5(c-8)(c-8)=3 equation: 


Simplifying
0.5(c + -8)(c + -8) = 3

Reorder the terms:
0.5(-8 + c)(c + -8) = 3

Reorder the terms:
0.5(-8 + c)(-8 + c) = 3

Multiply (-8 + c) * (-8 + c)
0.5(-8(-8 + c) + c(-8 + c)) = 3
0.5((-8 * -8 + c * -8) + c(-8 + c)) = 3
0.5((64 + -8c) + c(-8 + c)) = 3
0.5(64 + -8c + (-8 * c + c * c)) = 3
0.5(64 + -8c + (-8c + c2)) = 3

Combine like terms: -8c + -8c = -16c
0.5(64 + -16c + c2) = 3
(64 * 0.5 + -16c * 0.5 + c2 * 0.5) = 3
(32 + -8c + 0.5c2) = 3

Solving
32 + -8c + 0.5c2 = 3

Solving for variable 'c'.

Reorder the terms:
32 + -3 + -8c + 0.5c2 = 3 + -3

Combine like terms: 32 + -3 = 29
29 + -8c + 0.5c2 = 3 + -3

Combine like terms: 3 + -3 = 0
29 + -8c + 0.5c2 = 0

Begin completing the square.  Divide all terms by
0.5 the coefficient of the squared term: 

Divide each side by '0.5'.
58 + -16c + c2 = 0

Move the constant term to the right:

Add '-58' to each side of the equation.
58 + -16c + -58 + c2 = 0 + -58

Reorder the terms:
58 + -58 + -16c + c2 = 0 + -58

Combine like terms: 58 + -58 = 0
0 + -16c + c2 = 0 + -58
-16c + c2 = 0 + -58

Combine like terms: 0 + -58 = -58
-16c + c2 = -58

The c term is -16c.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16c + 64 + c2 = -58 + 64

Reorder the terms:
64 + -16c + c2 = -58 + 64

Combine like terms: -58 + 64 = 6
64 + -16c + c2 = 6

Factor a perfect square on the left side:
(c + -8)(c + -8) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(c + -8) equal to 2.449489743 and -2.449489743.


Subproblem 1
c + -8 = 2.449489743

Simplifying
c + -8 = 2.449489743

Reorder the terms:
-8 + c = 2.449489743

Solving
-8 + c = 2.449489743

Solving for variable 'c'.

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

Add '8' to each side of the equation.
-8 + 8 + c = 2.449489743 + 8

Combine like terms: -8 + 8 = 0
0 + c = 2.449489743 + 8
c = 2.449489743 + 8

Combine like terms: 2.449489743 + 8 = 10.449489743
c = 10.449489743

Simplifying
c = 10.449489743


Subproblem 2
c + -8 = -2.449489743

Simplifying
c + -8 = -2.449489743

Reorder the terms:
-8 + c = -2.449489743

Solving
-8 + c = -2.449489743

Solving for variable 'c'.

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

Add '8' to each side of the equation.
-8 + 8 + c = -2.449489743 + 8

Combine like terms: -8 + 8 = 0
0 + c = -2.449489743 + 8
c = -2.449489743 + 8

Combine like terms: -2.449489743 + 8 = 5.550510257
c = 5.550510257

Simplifying
c = 5.550510257


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {10.449489743, 5.550510257}

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