2(x^2+5x-133)=0

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Solution for 2(x^2+5x-133)=0 equation: 


Simplifying
2(x2 + 5x + -133) = 0

Reorder the terms:
2(-133 + 5x + x2) = 0
(-133 * 2 + 5x * 2 + x2 * 2) = 0
(-266 + 10x + 2x2) = 0

Solving
-266 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-133 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-133 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-133 + 5x + x2 = 0

Solving
-133 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '133' to each side of the equation.
-133 + 5x + 133 + x2 = 0 + 133

Reorder the terms:
-133 + 133 + 5x + x2 = 0 + 133

Combine like terms: -133 + 133 = 0
0 + 5x + x2 = 0 + 133
5x + x2 = 0 + 133

Combine like terms: 0 + 133 = 133
5x + x2 = 133

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 133 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 133 + 6.25

Combine like terms: 133 + 6.25 = 139.25
6.25 + 5x + x2 = 139.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 139.25

Calculate the square root of the right side: 11.800423721

Break this problem into two subproblems by setting 
(x + 2.5) equal to 11.800423721 and -11.800423721.


Subproblem 1
x + 2.5 = 11.800423721

Simplifying
x + 2.5 = 11.800423721

Reorder the terms:
2.5 + x = 11.800423721

Solving
2.5 + x = 11.800423721

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 11.800423721 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 11.800423721 + -2.5
x = 11.800423721 + -2.5

Combine like terms: 11.800423721 + -2.5 = 9.300423721
x = 9.300423721

Simplifying
x = 9.300423721


Subproblem 2
x + 2.5 = -11.800423721

Simplifying
x + 2.5 = -11.800423721

Reorder the terms:
2.5 + x = -11.800423721

Solving
2.5 + x = -11.800423721

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -11.800423721 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -11.800423721 + -2.5
x = -11.800423721 + -2.5

Combine like terms: -11.800423721 + -2.5 = -14.300423721
x = -14.300423721

Simplifying
x = -14.300423721


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.300423721, -14.300423721}
Solution
x = {9.300423721, -14.300423721}

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