2r^2+18r+37=3

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Solution for 2r^2+18r+37=3 equation: 


Simplifying
2r2 + 18r + 37 = 3

Reorder the terms:
37 + 18r + 2r2 = 3

Solving
37 + 18r + 2r2 = 3

Solving for variable 'r'.

Reorder the terms:
37 + -3 + 18r + 2r2 = 3 + -3

Combine like terms: 37 + -3 = 34
34 + 18r + 2r2 = 3 + -3

Combine like terms: 3 + -3 = 0
34 + 18r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + 9r + r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + 9r + r2)' equal to zero and attempt to solve:

Simplifying
17 + 9r + r2 = 0

Solving
17 + 9r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 9r + -17 + r2 = 0 + -17

Reorder the terms:
17 + -17 + 9r + r2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 9r + r2 = 0 + -17
9r + r2 = 0 + -17

Combine like terms: 0 + -17 = -17
9r + r2 = -17

The r term is 9r.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9r + 20.25 + r2 = -17 + 20.25

Reorder the terms:
20.25 + 9r + r2 = -17 + 20.25

Combine like terms: -17 + 20.25 = 3.25
20.25 + 9r + r2 = 3.25

Factor a perfect square on the left side:
(r + 4.5)(r + 4.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(r + 4.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
r + 4.5 = 1.802775638

Simplifying
r + 4.5 = 1.802775638

Reorder the terms:
4.5 + r = 1.802775638

Solving
4.5 + r = 1.802775638

Solving for variable 'r'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + r = 1.802775638 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + r = 1.802775638 + -4.5
r = 1.802775638 + -4.5

Combine like terms: 1.802775638 + -4.5 = -2.697224362
r = -2.697224362

Simplifying
r = -2.697224362


Subproblem 2
r + 4.5 = -1.802775638

Simplifying
r + 4.5 = -1.802775638

Reorder the terms:
4.5 + r = -1.802775638

Solving
4.5 + r = -1.802775638

Solving for variable 'r'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + r = -1.802775638 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + r = -1.802775638 + -4.5
r = -1.802775638 + -4.5

Combine like terms: -1.802775638 + -4.5 = -6.302775638
r = -6.302775638

Simplifying
r = -6.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-2.697224362, -6.302775638}
Solution
r = {-2.697224362, -6.302775638}

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