2x^2-12x-122=0

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Solution for 2x^2-12x-122=0 equation: 


Simplifying
2x2 + -12x + -122 = 0

Reorder the terms:
-122 + -12x + 2x2 = 0

Solving
-122 + -12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-61 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-61 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-61 + -6x + x2 = 0

Solving
-61 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + -6x + 61 + x2 = 0 + 61

Reorder the terms:
-61 + 61 + -6x + x2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + -6x + x2 = 0 + 61
-6x + x2 = 0 + 61

Combine like terms: 0 + 61 = 61
-6x + x2 = 61

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 = 61 + 9

Reorder the terms:
9 + -6x + x2 = 61 + 9

Combine like terms: 61 + 9 = 70
9 + -6x + x2 = 70

Factor a perfect square on the left side:
(x + -3)(x + -3) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + -3) equal to 8.366600265 and -8.366600265.


Subproblem 1
x + -3 = 8.366600265

Simplifying
x + -3 = 8.366600265

Reorder the terms:
-3 + x = 8.366600265

Solving
-3 + x = 8.366600265

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 = 8.366600265 + 3

Combine like terms: -3 + 3 = 0
0 + x = 8.366600265 + 3
x = 8.366600265 + 3

Combine like terms: 8.366600265 + 3 = 11.366600265
x = 11.366600265

Simplifying
x = 11.366600265


Subproblem 2
x + -3 = -8.366600265

Simplifying
x + -3 = -8.366600265

Reorder the terms:
-3 + x = -8.366600265

Solving
-3 + x = -8.366600265

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 = -8.366600265 + 3

Combine like terms: -3 + 3 = 0
0 + x = -8.366600265 + 3
x = -8.366600265 + 3

Combine like terms: -8.366600265 + 3 = -5.366600265
x = -5.366600265

Simplifying
x = -5.366600265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.366600265, -5.366600265}
Solution
x = {11.366600265, -5.366600265}

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