(r-5)(r+9)=-37

Solution for (r-5)(r+9)=-37 equation:

Simplifying
(r + -5)(r + 9) = -37

Reorder the terms:
(-5 + r)(r + 9) = -37

Reorder the terms:
(-5 + r)(9 + r) = -37

Multiply (-5 + r) * (9 + r)
(-5(9 + r) + r(9 + r)) = -37
((9 * -5 + r * -5) + r(9 + r)) = -37
((-45 + -5r) + r(9 + r)) = -37
(-45 + -5r + (9 * r + r * r)) = -37
(-45 + -5r + (9r + r2)) = -37

Combine like terms: -5r + 9r = 4r
(-45 + 4r + r2) = -37

Solving
-45 + 4r + r2 = -37

Solving for variable 'r'.

Reorder the terms:
-45 + 37 + 4r + r2 = -37 + 37

Combine like terms: -45 + 37 = -8
-8 + 4r + r2 = -37 + 37

Combine like terms: -37 + 37 = 0
-8 + 4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 4r + 8 + r2 = 0 + 8

Reorder the terms:
-8 + 8 + 4r + r2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 4r + r2 = 0 + 8
4r + r2 = 0 + 8

Combine like terms: 0 + 8 = 8
4r + r2 = 8

The r term is 4r.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4r + 4 + r2 = 8 + 4

Reorder the terms:
4 + 4r + r2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + 4r + r2 = 12

Factor a perfect square on the left side:
(r + 2)(r + 2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(r + 2) equal to 3.464101615 and -3.464101615.

Subproblem 1
r + 2 = 3.464101615

Simplifying
r + 2 = 3.464101615

Reorder the terms:
2 + r = 3.464101615

Solving
2 + r = 3.464101615

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = 3.464101615 + -2

Combine like terms: 2 + -2 = 0
0 + r = 3.464101615 + -2
r = 3.464101615 + -2

Combine like terms: 3.464101615 + -2 = 1.464101615
r = 1.464101615

Simplifying
r = 1.464101615

Subproblem 2
r + 2 = -3.464101615

Simplifying
r + 2 = -3.464101615

Reorder the terms:
2 + r = -3.464101615

Solving
2 + r = -3.464101615

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = -3.464101615 + -2

Combine like terms: 2 + -2 = 0
0 + r = -3.464101615 + -2
r = -3.464101615 + -2

Combine like terms: -3.464101615 + -2 = -5.464101615
r = -5.464101615

Simplifying
r = -5.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.464101615, -5.464101615}