x^2+2x-81=0

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


Simplifying
x2 + 2x + -81 = 0

Reorder the terms:
-81 + 2x + x2 = 0

Solving
-81 + 2x + 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 + 2x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + 2x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 2x + x2 = 0 + 81
2x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
2x + x2 = 81

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 81 + 1

Reorder the terms:
1 + 2x + x2 = 81 + 1

Combine like terms: 81 + 1 = 82
1 + 2x + x2 = 82

Factor a perfect square on the left side:
(x + 1)(x + 1) = 82

Calculate the square root of the right side: 9.055385138

Break this problem into two subproblems by setting 
(x + 1) equal to 9.055385138 and -9.055385138.

Subproblem 1

x + 1 = 9.055385138 Simplifying x + 1 = 9.055385138 Reorder the terms: 1 + x = 9.055385138 Solving 1 + x = 9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 9.055385138 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.055385138 + -1 x = 9.055385138 + -1 Combine like terms: 9.055385138 + -1 = 8.055385138 x = 8.055385138 Simplifying x = 8.055385138

Subproblem 2

x + 1 = -9.055385138 Simplifying x + 1 = -9.055385138 Reorder the terms: 1 + x = -9.055385138 Solving 1 + x = -9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -9.055385138 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.055385138 + -1 x = -9.055385138 + -1 Combine like terms: -9.055385138 + -1 = -10.055385138 x = -10.055385138 Simplifying x = -10.055385138

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.055385138, -10.055385138}

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