121r^2+242r-57=0

Solution for 121r^2+242r-57=0 equation:

Simplifying
121r2 + 242r + -57 = 0

Reorder the terms:
-57 + 242r + 121r2 = 0

Solving
-57 + 242r + 121r2 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
121 the coefficient of the squared term: 

Divide each side by '121'.
-0.4710743802 + 2r + r2 = 0

Move the constant term to the right:

Add '0.4710743802' to each side of the equation.
-0.4710743802 + 2r + 0.4710743802 + r2 = 0 + 0.4710743802

Reorder the terms:
-0.4710743802 + 0.4710743802 + 2r + r2 = 0 + 0.4710743802

Combine like terms: -0.4710743802 + 0.4710743802 = 0.0000000000
0.0000000000 + 2r + r2 = 0 + 0.4710743802
2r + r2 = 0 + 0.4710743802

Combine like terms: 0 + 0.4710743802 = 0.4710743802
2r + r2 = 0.4710743802

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 0.4710743802 + 1

Reorder the terms:
1 + 2r + r2 = 0.4710743802 + 1

Combine like terms: 0.4710743802 + 1 = 1.4710743802
1 + 2r + r2 = 1.4710743802

Factor a perfect square on the left side:
(r + 1)(r + 1) = 1.4710743802

Calculate the square root of the right side: 1.212878551

Break this problem into two subproblems by setting 
(r + 1) equal to 1.212878551 and -1.212878551.

Subproblem 1
r + 1 = 1.212878551

Simplifying
r + 1 = 1.212878551

Reorder the terms:
1 + r = 1.212878551

Solving
1 + r = 1.212878551

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = 1.212878551 + -1

Combine like terms: 1 + -1 = 0
0 + r = 1.212878551 + -1
r = 1.212878551 + -1

Combine like terms: 1.212878551 + -1 = 0.212878551
r = 0.212878551

Simplifying
r = 0.212878551

Subproblem 2
r + 1 = -1.212878551

Simplifying
r + 1 = -1.212878551

Reorder the terms:
1 + r = -1.212878551

Solving
1 + r = -1.212878551

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = -1.212878551 + -1

Combine like terms: 1 + -1 = 0
0 + r = -1.212878551 + -1
r = -1.212878551 + -1

Combine like terms: -1.212878551 + -1 = -2.212878551
r = -2.212878551

Simplifying
r = -2.212878551

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.212878551, -2.212878551}