r^2+2r-21=0

Solution for r^2+2r-21=0 equation:

Simplifying
r2 + 2r + -21 = 0

Reorder the terms:
-21 + 2r + r2 = 0

Solving
-21 + 2r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 2r + 21 + r2 = 0 + 21

Reorder the terms:
-21 + 21 + 2r + r2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2r + r2 = 0 + 21
2r + r2 = 0 + 21

Combine like terms: 0 + 21 = 21
2r + r2 = 21

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 = 21 + 1

Reorder the terms:
1 + 2r + r2 = 21 + 1

Combine like terms: 21 + 1 = 22
1 + 2r + r2 = 22

Factor a perfect square on the left side:
(r + 1)(r + 1) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(r + 1) equal to 4.69041576 and -4.69041576.

Subproblem 1
r + 1 = 4.69041576

Simplifying
r + 1 = 4.69041576

Reorder the terms:
1 + r = 4.69041576

Solving
1 + r = 4.69041576

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 = 4.69041576 + -1

Combine like terms: 1 + -1 = 0
0 + r = 4.69041576 + -1
r = 4.69041576 + -1

Combine like terms: 4.69041576 + -1 = 3.69041576
r = 3.69041576

Simplifying
r = 3.69041576

Subproblem 2
r + 1 = -4.69041576

Simplifying
r + 1 = -4.69041576

Reorder the terms:
1 + r = -4.69041576

Solving
1 + r = -4.69041576

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 = -4.69041576 + -1

Combine like terms: 1 + -1 = 0
0 + r = -4.69041576 + -1
r = -4.69041576 + -1

Combine like terms: -4.69041576 + -1 = -5.69041576
r = -5.69041576

Simplifying
r = -5.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.69041576, -5.69041576}