r^2-8r-21=0

Solution for r^2-8r-21=0 equation:

Simplifying
r2 + -8r + -21 = 0

Reorder the terms:
-21 + -8r + r2 = 0

Solving
-21 + -8r + 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 + -8r + 21 + r2 = 0 + 21

Reorder the terms:
-21 + 21 + -8r + r2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -8r + r2 = 0 + 21
-8r + r2 = 0 + 21

Combine like terms: 0 + 21 = 21
-8r + r2 = 21

The r term is -8r.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8r + 16 + r2 = 21 + 16

Reorder the terms:
16 + -8r + r2 = 21 + 16

Combine like terms: 21 + 16 = 37
16 + -8r + r2 = 37

Factor a perfect square on the left side:
(r + -4)(r + -4) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(r + -4) equal to 6.08276253 and -6.08276253.

Subproblem 1
r + -4 = 6.08276253

Simplifying
r + -4 = 6.08276253

Reorder the terms:
-4 + r = 6.08276253

Solving
-4 + r = 6.08276253

Solving for variable 'r'.

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

Add '4' to each side of the equation.
-4 + 4 + r = 6.08276253 + 4

Combine like terms: -4 + 4 = 0
0 + r = 6.08276253 + 4
r = 6.08276253 + 4

Combine like terms: 6.08276253 + 4 = 10.08276253
r = 10.08276253

Simplifying
r = 10.08276253

Subproblem 2
r + -4 = -6.08276253

Simplifying
r + -4 = -6.08276253

Reorder the terms:
-4 + r = -6.08276253

Solving
-4 + r = -6.08276253

Solving for variable 'r'.

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

Add '4' to each side of the equation.
-4 + 4 + r = -6.08276253 + 4

Combine like terms: -4 + 4 = 0
0 + r = -6.08276253 + 4
r = -6.08276253 + 4

Combine like terms: -6.08276253 + 4 = -2.08276253
r = -2.08276253

Simplifying
r = -2.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {10.08276253, -2.08276253}