2((2x^2)-11x-41)=0

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Solution for 2((2x^2)-11x-41)=0 equation: 


Simplifying
2((2x2) + -11x + -41) = 0

Reorder the terms:
2(-41 + -11x + (2x2)) = 0
(-41 * 2 + -11x * 2 + (2x2) * 2) = 0
(-82 + -22x + 4x2) = 0

Solving
-82 + -22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + -11x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-41 + -11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-41 + -11x + 2x2 = 0

Solving
-41 + -11x + 2x2 = 0

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

Divide each side by '2'.
-20.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '20.5' to each side of the equation.
-20.5 + -5.5x + 20.5 + x2 = 0 + 20.5

Reorder the terms:
-20.5 + 20.5 + -5.5x + x2 = 0 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + -5.5x + x2 = 0 + 20.5
-5.5x + x2 = 0 + 20.5

Combine like terms: 0 + 20.5 = 20.5
-5.5x + x2 = 20.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 20.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 20.5 + 7.5625

Combine like terms: 20.5 + 7.5625 = 28.0625
7.5625 + -5.5x + x2 = 28.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 28.0625

Calculate the square root of the right side: 5.297405025

Break this problem into two subproblems by setting 
(x + -2.75) equal to 5.297405025 and -5.297405025.


Subproblem 1
x + -2.75 = 5.297405025

Simplifying
x + -2.75 = 5.297405025

Reorder the terms:
-2.75 + x = 5.297405025

Solving
-2.75 + x = 5.297405025

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 5.297405025 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 5.297405025 + 2.75
x = 5.297405025 + 2.75

Combine like terms: 5.297405025 + 2.75 = 8.047405025
x = 8.047405025

Simplifying
x = 8.047405025


Subproblem 2
x + -2.75 = -5.297405025

Simplifying
x + -2.75 = -5.297405025

Reorder the terms:
-2.75 + x = -5.297405025

Solving
-2.75 + x = -5.297405025

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -5.297405025 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -5.297405025 + 2.75
x = -5.297405025 + 2.75

Combine like terms: -5.297405025 + 2.75 = -2.547405025
x = -2.547405025

Simplifying
x = -2.547405025


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.047405025, -2.547405025}
Solution
x = {8.047405025, -2.547405025}

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