x^2-2x=101

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Solution for x^2-2x=101 equation:


Simplifying
x2 + -2x = 101

Reorder the terms:
-2x + x2 = 101

Solving
-2x + x2 = 101

Solving for variable 'x'.

Reorder the terms:
-101 + -2x + x2 = 101 + -101

Combine like terms: 101 + -101 = 0
-101 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '101' to each side of the equation.
-101 + -2x + 101 + x2 = 0 + 101

Reorder the terms:
-101 + 101 + -2x + x2 = 0 + 101

Combine like terms: -101 + 101 = 0
0 + -2x + x2 = 0 + 101
-2x + x2 = 0 + 101

Combine like terms: 0 + 101 = 101
-2x + x2 = 101

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 101 + 1

Reorder the terms:
1 + -2x + x2 = 101 + 1

Combine like terms: 101 + 1 = 102
1 + -2x + x2 = 102

Factor a perfect square on the left side:
(x + -1)(x + -1) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(x + -1) equal to 10.099504938 and -10.099504938.

Subproblem 1

x + -1 = 10.099504938 Simplifying x + -1 = 10.099504938 Reorder the terms: -1 + x = 10.099504938 Solving -1 + x = 10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 10.099504938 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.099504938 + 1 x = 10.099504938 + 1 Combine like terms: 10.099504938 + 1 = 11.099504938 x = 11.099504938 Simplifying x = 11.099504938

Subproblem 2

x + -1 = -10.099504938 Simplifying x + -1 = -10.099504938 Reorder the terms: -1 + x = -10.099504938 Solving -1 + x = -10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -10.099504938 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.099504938 + 1 x = -10.099504938 + 1 Combine like terms: -10.099504938 + 1 = -9.099504938 x = -9.099504938 Simplifying x = -9.099504938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.099504938, -9.099504938}

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