2r^2+4r-232=0

Solution for 2r^2+4r-232=0 equation:

Simplifying
2r2 + 4r + -232 = 0

Reorder the terms:
-232 + 4r + 2r2 = 0

Solving
-232 + 4r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-116 + 2r + r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-116 + 2r + r2)' equal to zero and attempt to solve:

Simplifying
-116 + 2r + r2 = 0

Solving
-116 + 2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '116' to each side of the equation.
-116 + 2r + 116 + r2 = 0 + 116

Reorder the terms:
-116 + 116 + 2r + r2 = 0 + 116

Combine like terms: -116 + 116 = 0
0 + 2r + r2 = 0 + 116
2r + r2 = 0 + 116

Combine like terms: 0 + 116 = 116
2r + r2 = 116

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 = 116 + 1

Reorder the terms:
1 + 2r + r2 = 116 + 1

Combine like terms: 116 + 1 = 117
1 + 2r + r2 = 117

Factor a perfect square on the left side:
(r + 1)(r + 1) = 117

Calculate the square root of the right side: 10.816653826

Break this problem into two subproblems by setting 
(r + 1) equal to 10.816653826 and -10.816653826.

Subproblem 1
r + 1 = 10.816653826

Simplifying
r + 1 = 10.816653826

Reorder the terms:
1 + r = 10.816653826

Solving
1 + r = 10.816653826

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 = 10.816653826 + -1

Combine like terms: 1 + -1 = 0
0 + r = 10.816653826 + -1
r = 10.816653826 + -1

Combine like terms: 10.816653826 + -1 = 9.816653826
r = 9.816653826

Simplifying
r = 9.816653826

Subproblem 2
r + 1 = -10.816653826

Simplifying
r + 1 = -10.816653826

Reorder the terms:
1 + r = -10.816653826

Solving
1 + r = -10.816653826

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 = -10.816653826 + -1

Combine like terms: 1 + -1 = 0
0 + r = -10.816653826 + -1
r = -10.816653826 + -1

Combine like terms: -10.816653826 + -1 = -11.816653826
r = -11.816653826

Simplifying
r = -11.816653826

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.816653826, -11.816653826}
Solution
r = {9.816653826, -11.816653826}