x^2-81x-64=0

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Solution for x^2-81x-64=0 equation:


Simplifying
x2 + -81x + -64 = 0

Reorder the terms:
-64 + -81x + x2 = 0

Solving
-64 + -81x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -81x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + -81x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -81x + x2 = 0 + 64
-81x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
-81x + x2 = 64

The x term is -81x.  Take half its coefficient (-40.5).
Square it (1640.25) and add it to both sides.

Add '1640.25' to each side of the equation.
-81x + 1640.25 + x2 = 64 + 1640.25

Reorder the terms:
1640.25 + -81x + x2 = 64 + 1640.25

Combine like terms: 64 + 1640.25 = 1704.25
1640.25 + -81x + x2 = 1704.25

Factor a perfect square on the left side:
(x + -40.5)(x + -40.5) = 1704.25

Calculate the square root of the right side: 41.282562905

Break this problem into two subproblems by setting 
(x + -40.5) equal to 41.282562905 and -41.282562905.

Subproblem 1

x + -40.5 = 41.282562905 Simplifying x + -40.5 = 41.282562905 Reorder the terms: -40.5 + x = 41.282562905 Solving -40.5 + x = 41.282562905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = 41.282562905 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 41.282562905 + 40.5 x = 41.282562905 + 40.5 Combine like terms: 41.282562905 + 40.5 = 81.782562905 x = 81.782562905 Simplifying x = 81.782562905

Subproblem 2

x + -40.5 = -41.282562905 Simplifying x + -40.5 = -41.282562905 Reorder the terms: -40.5 + x = -41.282562905 Solving -40.5 + x = -41.282562905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = -41.282562905 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -41.282562905 + 40.5 x = -41.282562905 + 40.5 Combine like terms: -41.282562905 + 40.5 = -0.782562905 x = -0.782562905 Simplifying x = -0.782562905

Solution

The solution to the problem is based on the solutions from the subproblems. x = {81.782562905, -0.782562905}

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