4r^2+18r=-17

Solution for 4r^2+18r=-17 equation:

Simplifying
4r2 + 18r = -17

Reorder the terms:
18r + 4r2 = -17

Solving
18r + 4r2 = -17

Solving for variable 'r'.

Reorder the terms:
17 + 18r + 4r2 = -17 + 17

Combine like terms: -17 + 17 = 0
17 + 18r + 4r2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
4.25 + 4.5r + r2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + 4.5r + -4.25 + r2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + 4.5r + r2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + 4.5r + r2 = 0 + -4.25
4.5r + r2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
4.5r + r2 = -4.25

The r term is 4.5r.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5r + 5.0625 + r2 = -4.25 + 5.0625

Reorder the terms:
5.0625 + 4.5r + r2 = -4.25 + 5.0625

Combine like terms: -4.25 + 5.0625 = 0.8125
5.0625 + 4.5r + r2 = 0.8125

Factor a perfect square on the left side:
(r + 2.25)(r + 2.25) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(r + 2.25) equal to 0.901387819 and -0.901387819.

Subproblem 1
r + 2.25 = 0.901387819

Simplifying
r + 2.25 = 0.901387819

Reorder the terms:
2.25 + r = 0.901387819

Solving
2.25 + r = 0.901387819

Solving for variable 'r'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + r = 0.901387819 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + r = 0.901387819 + -2.25
r = 0.901387819 + -2.25

Combine like terms: 0.901387819 + -2.25 = -1.348612181
r = -1.348612181

Simplifying
r = -1.348612181

Subproblem 2
r + 2.25 = -0.901387819

Simplifying
r + 2.25 = -0.901387819

Reorder the terms:
2.25 + r = -0.901387819

Solving
2.25 + r = -0.901387819

Solving for variable 'r'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + r = -0.901387819 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + r = -0.901387819 + -2.25
r = -0.901387819 + -2.25

Combine like terms: -0.901387819 + -2.25 = -3.151387819
r = -3.151387819

Simplifying
r = -3.151387819

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-1.348612181, -3.151387819}