r^2+4r-23=0

Solution for r^2+4r-23=0 equation:

Simplifying
r2 + 4r + -23 = 0

Reorder the terms:
-23 + 4r + r2 = 0

Solving
-23 + 4r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 4r + 23 + r2 = 0 + 23

Reorder the terms:
-23 + 23 + 4r + r2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 4r + r2 = 0 + 23
4r + r2 = 0 + 23

Combine like terms: 0 + 23 = 23
4r + r2 = 23

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 = 23 + 4

Reorder the terms:
4 + 4r + r2 = 23 + 4

Combine like terms: 23 + 4 = 27
4 + 4r + r2 = 27

Factor a perfect square on the left side:
(r + 2)(r + 2) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(r + 2) equal to 5.196152423 and -5.196152423.

Subproblem 1
r + 2 = 5.196152423

Simplifying
r + 2 = 5.196152423

Reorder the terms:
2 + r = 5.196152423

Solving
2 + r = 5.196152423

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 = 5.196152423 + -2

Combine like terms: 2 + -2 = 0
0 + r = 5.196152423 + -2
r = 5.196152423 + -2

Combine like terms: 5.196152423 + -2 = 3.196152423
r = 3.196152423

Simplifying
r = 3.196152423

Subproblem 2
r + 2 = -5.196152423

Simplifying
r + 2 = -5.196152423

Reorder the terms:
2 + r = -5.196152423

Solving
2 + r = -5.196152423

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 = -5.196152423 + -2

Combine like terms: 2 + -2 = 0
0 + r = -5.196152423 + -2
r = -5.196152423 + -2

Combine like terms: -5.196152423 + -2 = -7.196152423
r = -7.196152423

Simplifying
r = -7.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.196152423, -7.196152423}