r^2+2r-28=0

Solution for r^2+2r-28=0 equation:

Simplifying
r2 + 2r + -28 = 0

Reorder the terms:
-28 + 2r + r2 = 0

Solving
-28 + 2r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 2r + 28 + r2 = 0 + 28

Reorder the terms:
-28 + 28 + 2r + r2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 2r + r2 = 0 + 28
2r + r2 = 0 + 28

Combine like terms: 0 + 28 = 28
2r + r2 = 28

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 = 28 + 1

Reorder the terms:
1 + 2r + r2 = 28 + 1

Combine like terms: 28 + 1 = 29
1 + 2r + r2 = 29

Factor a perfect square on the left side:
(r + 1)(r + 1) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(r + 1) equal to 5.385164807 and -5.385164807.

Subproblem 1
r + 1 = 5.385164807

Simplifying
r + 1 = 5.385164807

Reorder the terms:
1 + r = 5.385164807

Solving
1 + r = 5.385164807

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 = 5.385164807 + -1

Combine like terms: 1 + -1 = 0
0 + r = 5.385164807 + -1
r = 5.385164807 + -1

Combine like terms: 5.385164807 + -1 = 4.385164807
r = 4.385164807

Simplifying
r = 4.385164807

Subproblem 2
r + 1 = -5.385164807

Simplifying
r + 1 = -5.385164807

Reorder the terms:
1 + r = -5.385164807

Solving
1 + r = -5.385164807

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 = -5.385164807 + -1

Combine like terms: 1 + -1 = 0
0 + r = -5.385164807 + -1
r = -5.385164807 + -1

Combine like terms: -5.385164807 + -1 = -6.385164807
r = -6.385164807

Simplifying
r = -6.385164807

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.385164807, -6.385164807}