5r^2+10r-11=0

Solution for 5r^2+10r-11=0 equation:

Simplifying
5r2 + 10r + -11 = 0

Reorder the terms:
-11 + 10r + 5r2 = 0

Solving
-11 + 10r + 5r2 = 0

Solving for variable 'r'.

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

Divide each side by '5'.
-2.2 + 2r + r2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + 2r + 2.2 + r2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + 2r + r2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + 2r + r2 = 0 + 2.2
2r + r2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
2r + r2 = 2.2

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 = 2.2 + 1

Reorder the terms:
1 + 2r + r2 = 2.2 + 1

Combine like terms: 2.2 + 1 = 3.2
1 + 2r + r2 = 3.2

Factor a perfect square on the left side:
(r + 1)(r + 1) = 3.2

Calculate the square root of the right side: 1.788854382

Break this problem into two subproblems by setting 
(r + 1) equal to 1.788854382 and -1.788854382.

Subproblem 1
r + 1 = 1.788854382

Simplifying
r + 1 = 1.788854382

Reorder the terms:
1 + r = 1.788854382

Solving
1 + r = 1.788854382

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 = 1.788854382 + -1

Combine like terms: 1 + -1 = 0
0 + r = 1.788854382 + -1
r = 1.788854382 + -1

Combine like terms: 1.788854382 + -1 = 0.788854382
r = 0.788854382

Simplifying
r = 0.788854382

Subproblem 2
r + 1 = -1.788854382

Simplifying
r + 1 = -1.788854382

Reorder the terms:
1 + r = -1.788854382

Solving
1 + r = -1.788854382

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 = -1.788854382 + -1

Combine like terms: 1 + -1 = 0
0 + r = -1.788854382 + -1
r = -1.788854382 + -1

Combine like terms: -1.788854382 + -1 = -2.788854382
r = -2.788854382

Simplifying
r = -2.788854382

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.788854382, -2.788854382}