x^2-16x-81=0

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Solution for x^2-16x-81=0 equation:


Simplifying
x2 + -16x + -81 = 0

Reorder the terms:
-81 + -16x + x2 = 0

Solving
-81 + -16x + 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 + -16x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + -16x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -16x + x2 = 0 + 81
-16x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
-16x + x2 = 81

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 81 + 64

Reorder the terms:
64 + -16x + x2 = 81 + 64

Combine like terms: 81 + 64 = 145
64 + -16x + x2 = 145

Factor a perfect square on the left side:
(x + -8)(x + -8) = 145

Calculate the square root of the right side: 12.041594579

Break this problem into two subproblems by setting 
(x + -8) equal to 12.041594579 and -12.041594579.

Subproblem 1

x + -8 = 12.041594579 Simplifying x + -8 = 12.041594579 Reorder the terms: -8 + x = 12.041594579 Solving -8 + x = 12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 12.041594579 + 8 Combine like terms: -8 + 8 = 0 0 + x = 12.041594579 + 8 x = 12.041594579 + 8 Combine like terms: 12.041594579 + 8 = 20.041594579 x = 20.041594579 Simplifying x = 20.041594579

Subproblem 2

x + -8 = -12.041594579 Simplifying x + -8 = -12.041594579 Reorder the terms: -8 + x = -12.041594579 Solving -8 + x = -12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -12.041594579 + 8 Combine like terms: -8 + 8 = 0 0 + x = -12.041594579 + 8 x = -12.041594579 + 8 Combine like terms: -12.041594579 + 8 = -4.041594579 x = -4.041594579 Simplifying x = -4.041594579

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.041594579, -4.041594579}

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