4r^2+18r=-16

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Solution for 4r^2+18r=-16 equation: 


Simplifying
4r2 + 18r = -16

Reorder the terms:
18r + 4r2 = -16

Solving
18r + 4r2 = -16

Solving for variable 'r'.

Reorder the terms:
16 + 18r + 4r2 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + 18r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 9r + 2r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + 9r + 2r2)' equal to zero and attempt to solve:

Simplifying
8 + 9r + 2r2 = 0

Solving
8 + 9r + 2r2 = 0

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

Divide each side by '2'.
4 + 4.5r + r2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 4.5r + -4 + r2 = 0 + -4

Reorder the terms:
4 + -4 + 4.5r + r2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 4.5r + r2 = 0 + -4
4.5r + r2 = 0 + -4

Combine like terms: 0 + -4 = -4
4.5r + r2 = -4

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 + 5.0625

Reorder the terms:
5.0625 + 4.5r + r2 = -4 + 5.0625

Combine like terms: -4 + 5.0625 = 1.0625
5.0625 + 4.5r + r2 = 1.0625

Factor a perfect square on the left side:
(r + 2.25)(r + 2.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(r + 2.25) equal to 1.030776406 and -1.030776406.


Subproblem 1
r + 2.25 = 1.030776406

Simplifying
r + 2.25 = 1.030776406

Reorder the terms:
2.25 + r = 1.030776406

Solving
2.25 + r = 1.030776406

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 = 1.030776406 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + r = 1.030776406 + -2.25
r = 1.030776406 + -2.25

Combine like terms: 1.030776406 + -2.25 = -1.219223594
r = -1.219223594

Simplifying
r = -1.219223594


Subproblem 2
r + 2.25 = -1.030776406

Simplifying
r + 2.25 = -1.030776406

Reorder the terms:
2.25 + r = -1.030776406

Solving
2.25 + r = -1.030776406

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 = -1.030776406 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + r = -1.030776406 + -2.25
r = -1.030776406 + -2.25

Combine like terms: -1.030776406 + -2.25 = -3.280776406
r = -3.280776406

Simplifying
r = -3.280776406


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-1.219223594, -3.280776406}
Solution
r = {-1.219223594, -3.280776406}

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