x^2+82x-81=0

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Solution for x^2+82x-81=0 equation:


Simplifying
x2 + 82x + -81 = 0

Reorder the terms:
-81 + 82x + x2 = 0

Solving
-81 + 82x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 82x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + 82x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 82x + x2 = 0 + 81
82x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
82x + x2 = 81

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 = 81 + 1681

Reorder the terms:
1681 + 82x + x2 = 81 + 1681

Combine like terms: 81 + 1681 = 1762
1681 + 82x + x2 = 1762

Factor a perfect square on the left side:
(x + 41)(x + 41) = 1762

Calculate the square root of the right side: 41.976183724

Break this problem into two subproblems by setting 
(x + 41) equal to 41.976183724 and -41.976183724.

Subproblem 1

x + 41 = 41.976183724 Simplifying x + 41 = 41.976183724 Reorder the terms: 41 + x = 41.976183724 Solving 41 + x = 41.976183724 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 = 41.976183724 + -41 Combine like terms: 41 + -41 = 0 0 + x = 41.976183724 + -41 x = 41.976183724 + -41 Combine like terms: 41.976183724 + -41 = 0.976183724 x = 0.976183724 Simplifying x = 0.976183724

Subproblem 2

x + 41 = -41.976183724 Simplifying x + 41 = -41.976183724 Reorder the terms: 41 + x = -41.976183724 Solving 41 + x = -41.976183724 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 = -41.976183724 + -41 Combine like terms: 41 + -41 = 0 0 + x = -41.976183724 + -41 x = -41.976183724 + -41 Combine like terms: -41.976183724 + -41 = -82.976183724 x = -82.976183724 Simplifying x = -82.976183724

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.976183724, -82.976183724}

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