r^2+r-121=0

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Solution for r^2+r-121=0 equation: 


Simplifying
r2 + r + -121 = 0

Reorder the terms:
-121 + r + r2 = 0

Solving
-121 + r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '121' to each side of the equation.
-121 + r + 121 + r2 = 0 + 121

Reorder the terms:
-121 + 121 + r + r2 = 0 + 121

Combine like terms: -121 + 121 = 0
0 + r + r2 = 0 + 121
r + r2 = 0 + 121

Combine like terms: 0 + 121 = 121
r + r2 = 121

The r term is r.  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.
r + 0.25 + r2 = 121 + 0.25

Reorder the terms:
0.25 + r + r2 = 121 + 0.25

Combine like terms: 121 + 0.25 = 121.25
0.25 + r + r2 = 121.25

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

Calculate the square root of the right side: 11.011357773

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


Subproblem 1
r + 0.5 = 11.011357773

Simplifying
r + 0.5 = 11.011357773

Reorder the terms:
0.5 + r = 11.011357773

Solving
0.5 + r = 11.011357773

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 11.011357773 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 11.011357773 + -0.5
r = 11.011357773 + -0.5

Combine like terms: 11.011357773 + -0.5 = 10.511357773
r = 10.511357773

Simplifying
r = 10.511357773


Subproblem 2
r + 0.5 = -11.011357773

Simplifying
r + 0.5 = -11.011357773

Reorder the terms:
0.5 + r = -11.011357773

Solving
0.5 + r = -11.011357773

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -11.011357773 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -11.011357773 + -0.5
r = -11.011357773 + -0.5

Combine like terms: -11.011357773 + -0.5 = -11.511357773
r = -11.511357773

Simplifying
r = -11.511357773


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

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