x^2-2x=26

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Solution for x^2-2x=26 equation:


Simplifying
x2 + -2x = 26

Reorder the terms:
-2x + x2 = 26

Solving
-2x + x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + -2x + x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -2x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + -2x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -2x + x2 = 0 + 26
-2x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
-2x + x2 = 26

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 = 26 + 1

Reorder the terms:
1 + -2x + x2 = 26 + 1

Combine like terms: 26 + 1 = 27
1 + -2x + x2 = 27

Factor a perfect square on the left side:
(x + -1)(x + -1) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + -1) equal to 5.196152423 and -5.196152423.

Subproblem 1

x + -1 = 5.196152423 Simplifying x + -1 = 5.196152423 Reorder the terms: -1 + x = 5.196152423 Solving -1 + x = 5.196152423 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 = 5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.196152423 + 1 x = 5.196152423 + 1 Combine like terms: 5.196152423 + 1 = 6.196152423 x = 6.196152423 Simplifying x = 6.196152423

Subproblem 2

x + -1 = -5.196152423 Simplifying x + -1 = -5.196152423 Reorder the terms: -1 + x = -5.196152423 Solving -1 + x = -5.196152423 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 = -5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.196152423 + 1 x = -5.196152423 + 1 Combine like terms: -5.196152423 + 1 = -4.196152423 x = -4.196152423 Simplifying x = -4.196152423

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.196152423, -4.196152423}

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