x^2+82x-2320=0

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Solution for x^2+82x-2320=0 equation: 


Simplifying
x2 + 82x + -2320 = 0

Reorder the terms:
-2320 + 82x + x2 = 0

Solving
-2320 + 82x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2320' to each side of the equation.
-2320 + 82x + 2320 + x2 = 0 + 2320

Reorder the terms:
-2320 + 2320 + 82x + x2 = 0 + 2320

Combine like terms: -2320 + 2320 = 0
0 + 82x + x2 = 0 + 2320
82x + x2 = 0 + 2320

Combine like terms: 0 + 2320 = 2320
82x + x2 = 2320

The x term is 82x.  Take half its coefficient (41).
Square it (1681) and add it to both sides.

Add '1681' to each side of the equation.
82x + 1681 + x2 = 2320 + 1681

Reorder the terms:
1681 + 82x + x2 = 2320 + 1681

Combine like terms: 2320 + 1681 = 4001
1681 + 82x + x2 = 4001

Factor a perfect square on the left side:
(x + 41)(x + 41) = 4001

Calculate the square root of the right side: 63.253458403

Break this problem into two subproblems by setting 
(x + 41) equal to 63.253458403 and -63.253458403.


Subproblem 1
x + 41 = 63.253458403

Simplifying
x + 41 = 63.253458403

Reorder the terms:
41 + x = 63.253458403

Solving
41 + x = 63.253458403

Solving for variable 'x'.

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

Add '-41' to each side of the equation.
41 + -41 + x = 63.253458403 + -41

Combine like terms: 41 + -41 = 0
0 + x = 63.253458403 + -41
x = 63.253458403 + -41

Combine like terms: 63.253458403 + -41 = 22.253458403
x = 22.253458403

Simplifying
x = 22.253458403


Subproblem 2
x + 41 = -63.253458403

Simplifying
x + 41 = -63.253458403

Reorder the terms:
41 + x = -63.253458403

Solving
41 + x = -63.253458403

Solving for variable 'x'.

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

Add '-41' to each side of the equation.
41 + -41 + x = -63.253458403 + -41

Combine like terms: 41 + -41 = 0
0 + x = -63.253458403 + -41
x = -63.253458403 + -41

Combine like terms: -63.253458403 + -41 = -104.253458403
x = -104.253458403

Simplifying
x = -104.253458403


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.253458403, -104.253458403}

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