.5(x-11)(x-11)+12=30

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Solution for .5(x-11)(x-11)+12=30 equation: 


Simplifying
0.5(x + -11)(x + -11) + 12 = 30

Reorder the terms:
0.5(-11 + x)(x + -11) + 12 = 30

Reorder the terms:
0.5(-11 + x)(-11 + x) + 12 = 30

Multiply (-11 + x) * (-11 + x)
0.5(-11(-11 + x) + x(-11 + x)) + 12 = 30
0.5((-11 * -11 + x * -11) + x(-11 + x)) + 12 = 30
0.5((121 + -11x) + x(-11 + x)) + 12 = 30
0.5(121 + -11x + (-11 * x + x * x)) + 12 = 30
0.5(121 + -11x + (-11x + x2)) + 12 = 30

Combine like terms: -11x + -11x = -22x
0.5(121 + -22x + x2) + 12 = 30
(121 * 0.5 + -22x * 0.5 + x2 * 0.5) + 12 = 30
(60.5 + -11x + 0.5x2) + 12 = 30

Reorder the terms:
60.5 + 12 + -11x + 0.5x2 = 30

Combine like terms: 60.5 + 12 = 72.5
72.5 + -11x + 0.5x2 = 30

Solving
72.5 + -11x + 0.5x2 = 30

Solving for variable 'x'.

Reorder the terms:
72.5 + -30 + -11x + 0.5x2 = 30 + -30

Combine like terms: 72.5 + -30 = 42.5
42.5 + -11x + 0.5x2 = 30 + -30

Combine like terms: 30 + -30 = 0
42.5 + -11x + 0.5x2 = 0

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

Divide each side by '0.5'.
85 + -22x + x2 = 0

Move the constant term to the right:

Add '-85' to each side of the equation.
85 + -22x + -85 + x2 = 0 + -85

Reorder the terms:
85 + -85 + -22x + x2 = 0 + -85

Combine like terms: 85 + -85 = 0
0 + -22x + x2 = 0 + -85
-22x + x2 = 0 + -85

Combine like terms: 0 + -85 = -85
-22x + x2 = -85

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = -85 + 121

Reorder the terms:
121 + -22x + x2 = -85 + 121

Combine like terms: -85 + 121 = 36
121 + -22x + x2 = 36

Factor a perfect square on the left side:
(x + -11)(x + -11) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + -11) equal to 6 and -6.


Subproblem 1
x + -11 = 6

Simplifying
x + -11 = 6

Reorder the terms:
-11 + x = 6

Solving
-11 + x = 6

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 6 + 11

Combine like terms: -11 + 11 = 0
0 + x = 6 + 11
x = 6 + 11

Combine like terms: 6 + 11 = 17
x = 17

Simplifying
x = 17


Subproblem 2
x + -11 = -6

Simplifying
x + -11 = -6

Reorder the terms:
-11 + x = -6

Solving
-11 + x = -6

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -6 + 11

Combine like terms: -11 + 11 = 0
0 + x = -6 + 11
x = -6 + 11

Combine like terms: -6 + 11 = 5
x = 5

Simplifying
x = 5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17, 5}

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