x^2-10*x-81=0

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Solution for x^2-10*x-81=0 equation:


Simplifying
x2 + -10x + -81 = 0

Reorder the terms:
-81 + -10x + x2 = 0

Solving
-81 + -10x + 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 + -10x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + -10x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -10x + x2 = 0 + 81
-10x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
-10x + x2 = 81

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 81 + 25

Reorder the terms:
25 + -10x + x2 = 81 + 25

Combine like terms: 81 + 25 = 106
25 + -10x + x2 = 106

Factor a perfect square on the left side:
(x + -5)(x + -5) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + -5) equal to 10.295630141 and -10.295630141.


Subproblem 1
x + -5 = 10.295630141

Simplifying
x + -5 = 10.295630141

Reorder the terms:
-5 + x = 10.295630141

Solving
-5 + x = 10.295630141

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + x = 10.295630141 + 5

Combine like terms: -5 + 5 = 0
0 + x = 10.295630141 + 5
x = 10.295630141 + 5

Combine like terms: 10.295630141 + 5 = 15.295630141
x = 15.295630141

Simplifying
x = 15.295630141


Subproblem 2
x + -5 = -10.295630141

Simplifying
x + -5 = -10.295630141

Reorder the terms:
-5 + x = -10.295630141

Solving
-5 + x = -10.295630141

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + x = -10.295630141 + 5

Combine like terms: -5 + 5 = 0
0 + x = -10.295630141 + 5
x = -10.295630141 + 5

Combine like terms: -10.295630141 + 5 = -5.295630141
x = -5.295630141

Simplifying
x = -5.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.295630141, -5.295630141}

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