x^2-x-180=0

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Solution for x^2-x-180=0 equation:


Simplifying
x2 + -1x + -180 = 0

Reorder the terms:
-180 + -1x + x2 = 0

Solving
-180 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + -1x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + -1x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -1x + x2 = 0 + 180
-1x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
-1x + x2 = 180

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 = 180 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 180 + 0.25

Combine like terms: 180 + 0.25 = 180.25
0.25 + -1x + x2 = 180.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 180.25

Calculate the square root of the right side: 13.425721582

Break this problem into two subproblems by setting 
(x + -0.5) equal to 13.425721582 and -13.425721582.

Subproblem 1

x + -0.5 = 13.425721582 Simplifying x + -0.5 = 13.425721582 Reorder the terms: -0.5 + x = 13.425721582 Solving -0.5 + x = 13.425721582 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 = 13.425721582 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 13.425721582 + 0.5 x = 13.425721582 + 0.5 Combine like terms: 13.425721582 + 0.5 = 13.925721582 x = 13.925721582 Simplifying x = 13.925721582

Subproblem 2

x + -0.5 = -13.425721582 Simplifying x + -0.5 = -13.425721582 Reorder the terms: -0.5 + x = -13.425721582 Solving -0.5 + x = -13.425721582 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 = -13.425721582 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -13.425721582 + 0.5 x = -13.425721582 + 0.5 Combine like terms: -13.425721582 + 0.5 = -12.925721582 x = -12.925721582 Simplifying x = -12.925721582

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.925721582, -12.925721582}

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