2x^2-8x-82=0

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Solution for 2x^2-8x-82=0 equation: 


Simplifying
2x2 + -8x + -82 = 0

Reorder the terms:
-82 + -8x + 2x2 = 0

Solving
-82 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-41 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-41 + -4x + x2 = 0

Solving
-41 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + -4x + 41 + x2 = 0 + 41

Reorder the terms:
-41 + 41 + -4x + x2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -4x + x2 = 0 + 41
-4x + x2 = 0 + 41

Combine like terms: 0 + 41 = 41
-4x + x2 = 41

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 41 + 4

Reorder the terms:
4 + -4x + x2 = 41 + 4

Combine like terms: 41 + 4 = 45
4 + -4x + x2 = 45

Factor a perfect square on the left side:
(x + -2)(x + -2) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + -2) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + -2 = 6.708203933

Simplifying
x + -2 = 6.708203933

Reorder the terms:
-2 + x = 6.708203933

Solving
-2 + x = 6.708203933

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 6.708203933 + 2

Combine like terms: -2 + 2 = 0
0 + x = 6.708203933 + 2
x = 6.708203933 + 2

Combine like terms: 6.708203933 + 2 = 8.708203933
x = 8.708203933

Simplifying
x = 8.708203933


Subproblem 2
x + -2 = -6.708203933

Simplifying
x + -2 = -6.708203933

Reorder the terms:
-2 + x = -6.708203933

Solving
-2 + x = -6.708203933

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -6.708203933 + 2

Combine like terms: -2 + 2 = 0
0 + x = -6.708203933 + 2
x = -6.708203933 + 2

Combine like terms: -6.708203933 + 2 = -4.708203933
x = -4.708203933

Simplifying
x = -4.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.708203933, -4.708203933}
Solution
x = {8.708203933, -4.708203933}

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