x^2-2x=65

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Solution for x^2-2x=65 equation:


Simplifying
x2 + -2x = 65

Reorder the terms:
-2x + x2 = 65

Solving
-2x + x2 = 65

Solving for variable 'x'.

Reorder the terms:
-65 + -2x + x2 = 65 + -65

Combine like terms: 65 + -65 = 0
-65 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + -2x + 65 + x2 = 0 + 65

Reorder the terms:
-65 + 65 + -2x + x2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + -2x + x2 = 0 + 65
-2x + x2 = 0 + 65

Combine like terms: 0 + 65 = 65
-2x + x2 = 65

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 = 65 + 1

Reorder the terms:
1 + -2x + x2 = 65 + 1

Combine like terms: 65 + 1 = 66
1 + -2x + x2 = 66

Factor a perfect square on the left side:
(x + -1)(x + -1) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(x + -1) equal to 8.124038405 and -8.124038405.

Subproblem 1

x + -1 = 8.124038405 Simplifying x + -1 = 8.124038405 Reorder the terms: -1 + x = 8.124038405 Solving -1 + x = 8.124038405 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 = 8.124038405 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.124038405 + 1 x = 8.124038405 + 1 Combine like terms: 8.124038405 + 1 = 9.124038405 x = 9.124038405 Simplifying x = 9.124038405

Subproblem 2

x + -1 = -8.124038405 Simplifying x + -1 = -8.124038405 Reorder the terms: -1 + x = -8.124038405 Solving -1 + x = -8.124038405 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 = -8.124038405 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.124038405 + 1 x = -8.124038405 + 1 Combine like terms: -8.124038405 + 1 = -7.124038405 x = -7.124038405 Simplifying x = -7.124038405

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.124038405, -7.124038405}

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