x^2+4x-4=81

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Solution for x^2+4x-4=81 equation:


Simplifying
x2 + 4x + -4 = 81

Reorder the terms:
-4 + 4x + x2 = 81

Solving
-4 + 4x + x2 = 81

Solving for variable 'x'.

Reorder the terms:
-4 + -81 + 4x + x2 = 81 + -81

Combine like terms: -4 + -81 = -85
-85 + 4x + x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-85 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + 4x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + 4x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + 4x + x2 = 0 + 85
4x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
4x + x2 = 85

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 = 85 + 4

Reorder the terms:
4 + 4x + x2 = 85 + 4

Combine like terms: 85 + 4 = 89
4 + 4x + x2 = 89

Factor a perfect square on the left side:
(x + 2)(x + 2) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(x + 2) equal to 9.433981132 and -9.433981132.

Subproblem 1

x + 2 = 9.433981132 Simplifying x + 2 = 9.433981132 Reorder the terms: 2 + x = 9.433981132 Solving 2 + x = 9.433981132 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 = 9.433981132 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.433981132 + -2 x = 9.433981132 + -2 Combine like terms: 9.433981132 + -2 = 7.433981132 x = 7.433981132 Simplifying x = 7.433981132

Subproblem 2

x + 2 = -9.433981132 Simplifying x + 2 = -9.433981132 Reorder the terms: 2 + x = -9.433981132 Solving 2 + x = -9.433981132 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 = -9.433981132 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.433981132 + -2 x = -9.433981132 + -2 Combine like terms: -9.433981132 + -2 = -11.433981132 x = -11.433981132 Simplifying x = -11.433981132

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.433981132, -11.433981132}

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