2x^2-12x+18+6=86

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Solution for 2x^2-12x+18+6=86 equation: 


Simplifying
2x2 + -12x + 18 + 6 = 86

Reorder the terms:
18 + 6 + -12x + 2x2 = 86

Combine like terms: 18 + 6 = 24
24 + -12x + 2x2 = 86

Solving
24 + -12x + 2x2 = 86

Solving for variable 'x'.

Reorder the terms:
24 + -86 + -12x + 2x2 = 86 + -86

Combine like terms: 24 + -86 = -62
-62 + -12x + 2x2 = 86 + -86

Combine like terms: 86 + -86 = 0
-62 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-31 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-31 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-31 + -6x + x2 = 0

Solving
-31 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -6x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + -6x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -6x + x2 = 0 + 31
-6x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
-6x + x2 = 31

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 31 + 9

Reorder the terms:
9 + -6x + x2 = 31 + 9

Combine like terms: 31 + 9 = 40
9 + -6x + x2 = 40

Factor a perfect square on the left side:
(x + -3)(x + -3) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -3) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + -3 = 6.32455532

Simplifying
x + -3 = 6.32455532

Reorder the terms:
-3 + x = 6.32455532

Solving
-3 + x = 6.32455532

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 6.32455532 + 3

Combine like terms: -3 + 3 = 0
0 + x = 6.32455532 + 3
x = 6.32455532 + 3

Combine like terms: 6.32455532 + 3 = 9.32455532
x = 9.32455532

Simplifying
x = 9.32455532


Subproblem 2
x + -3 = -6.32455532

Simplifying
x + -3 = -6.32455532

Reorder the terms:
-3 + x = -6.32455532

Solving
-3 + x = -6.32455532

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -6.32455532 + 3

Combine like terms: -3 + 3 = 0
0 + x = -6.32455532 + 3
x = -6.32455532 + 3

Combine like terms: -6.32455532 + 3 = -3.32455532
x = -3.32455532

Simplifying
x = -3.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.32455532, -3.32455532}
Solution
x = {9.32455532, -3.32455532}

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