x^2-x-121=0

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Solution for x^2-x-121=0 equation:


Simplifying
x2 + -1x + -121 = 0

Reorder the terms:
-121 + -1x + x2 = 0

Solving
-121 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '121' to each side of the equation.
-121 + -1x + 121 + x2 = 0 + 121

Reorder the terms:
-121 + 121 + -1x + x2 = 0 + 121

Combine like terms: -121 + 121 = 0
0 + -1x + x2 = 0 + 121
-1x + x2 = 0 + 121

Combine like terms: 0 + 121 = 121
-1x + x2 = 121

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 = 121 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 121 + 0.25

Combine like terms: 121 + 0.25 = 121.25
0.25 + -1x + x2 = 121.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 121.25

Calculate the square root of the right side: 11.011357773

Break this problem into two subproblems by setting 
(x + -0.5) equal to 11.011357773 and -11.011357773.

Subproblem 1

x + -0.5 = 11.011357773 Simplifying x + -0.5 = 11.011357773 Reorder the terms: -0.5 + x = 11.011357773 Solving -0.5 + x = 11.011357773 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 = 11.011357773 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 11.011357773 + 0.5 x = 11.011357773 + 0.5 Combine like terms: 11.011357773 + 0.5 = 11.511357773 x = 11.511357773 Simplifying x = 11.511357773

Subproblem 2

x + -0.5 = -11.011357773 Simplifying x + -0.5 = -11.011357773 Reorder the terms: -0.5 + x = -11.011357773 Solving -0.5 + x = -11.011357773 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 = -11.011357773 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -11.011357773 + 0.5 x = -11.011357773 + 0.5 Combine like terms: -11.011357773 + 0.5 = -10.511357773 x = -10.511357773 Simplifying x = -10.511357773

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.511357773, -10.511357773}

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