x^2-2x+1=81-x

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Solution for x^2-2x+1=81-x equation:


Simplifying
x2 + -2x + 1 = 81 + -1x

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

Solving
1 + -2x + x2 = 81 + -1x

Solving for variable 'x'.

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

Combine like terms: 1 + -81 = -80
-80 + -2x + x + x2 = 81 + -1x + -81 + x

Combine like terms: -2x + x = -1x
-80 + -1x + x2 = 81 + -1x + -81 + x

Reorder the terms:
-80 + -1x + x2 = 81 + -81 + -1x + x

Combine like terms: 81 + -81 = 0
-80 + -1x + x2 = 0 + -1x + x
-80 + -1x + x2 = -1x + x

Combine like terms: -1x + x = 0
-80 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -1x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -1x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -1x + x2 = 0 + 80
-1x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-1x + x2 = 80

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 80 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 80 + 0.25

Combine like terms: 80 + 0.25 = 80.25
0.25 + -1x + x2 = 80.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 80.25

Calculate the square root of the right side: 8.958236434

Break this problem into two subproblems by setting 
(x + -0.5) equal to 8.958236434 and -8.958236434.

Subproblem 1

x + -0.5 = 8.958236434 Simplifying x + -0.5 = 8.958236434 Reorder the terms: -0.5 + x = 8.958236434 Solving -0.5 + x = 8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 8.958236434 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.958236434 + 0.5 x = 8.958236434 + 0.5 Combine like terms: 8.958236434 + 0.5 = 9.458236434 x = 9.458236434 Simplifying x = 9.458236434

Subproblem 2

x + -0.5 = -8.958236434 Simplifying x + -0.5 = -8.958236434 Reorder the terms: -0.5 + x = -8.958236434 Solving -0.5 + x = -8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -8.958236434 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.958236434 + 0.5 x = -8.958236434 + 0.5 Combine like terms: -8.958236434 + 0.5 = -8.458236434 x = -8.458236434 Simplifying x = -8.458236434

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.458236434, -8.458236434}

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