2x^2+20x-122=0

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Solution for 2x^2+20x-122=0 equation: 


Simplifying
2x2 + 20x + -122 = 0

Reorder the terms:
-122 + 20x + 2x2 = 0

Solving
-122 + 20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-61 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-61 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-61 + 10x + x2 = 0

Solving
-61 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + 10x + 61 + x2 = 0 + 61

Reorder the terms:
-61 + 61 + 10x + x2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + 10x + x2 = 0 + 61
10x + x2 = 0 + 61

Combine like terms: 0 + 61 = 61
10x + x2 = 61

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 61 + 25

Reorder the terms:
25 + 10x + x2 = 61 + 25

Combine like terms: 61 + 25 = 86
25 + 10x + x2 = 86

Factor a perfect square on the left side:
(x + 5)(x + 5) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(x + 5) equal to 9.273618495 and -9.273618495.


Subproblem 1
x + 5 = 9.273618495

Simplifying
x + 5 = 9.273618495

Reorder the terms:
5 + x = 9.273618495

Solving
5 + x = 9.273618495

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 9.273618495 + -5

Combine like terms: 5 + -5 = 0
0 + x = 9.273618495 + -5
x = 9.273618495 + -5

Combine like terms: 9.273618495 + -5 = 4.273618495
x = 4.273618495

Simplifying
x = 4.273618495


Subproblem 2
x + 5 = -9.273618495

Simplifying
x + 5 = -9.273618495

Reorder the terms:
5 + x = -9.273618495

Solving
5 + x = -9.273618495

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -9.273618495 + -5

Combine like terms: 5 + -5 = 0
0 + x = -9.273618495 + -5
x = -9.273618495 + -5

Combine like terms: -9.273618495 + -5 = -14.273618495
x = -14.273618495

Simplifying
x = -14.273618495


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.273618495, -14.273618495}
Solution
x = {4.273618495, -14.273618495}

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