r^2+3r-396=0

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Solution for r^2+3r-396=0 equation: 


Simplifying
r2 + 3r + -396 = 0

Reorder the terms:
-396 + 3r + r2 = 0

Solving
-396 + 3r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '396' to each side of the equation.
-396 + 3r + 396 + r2 = 0 + 396

Reorder the terms:
-396 + 396 + 3r + r2 = 0 + 396

Combine like terms: -396 + 396 = 0
0 + 3r + r2 = 0 + 396
3r + r2 = 0 + 396

Combine like terms: 0 + 396 = 396
3r + r2 = 396

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 396 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 396 + 2.25

Combine like terms: 396 + 2.25 = 398.25
2.25 + 3r + r2 = 398.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 398.25

Calculate the square root of the right side: 19.956202043

Break this problem into two subproblems by setting 
(r + 1.5) equal to 19.956202043 and -19.956202043.


Subproblem 1
r + 1.5 = 19.956202043

Simplifying
r + 1.5 = 19.956202043

Reorder the terms:
1.5 + r = 19.956202043

Solving
1.5 + r = 19.956202043

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = 19.956202043 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = 19.956202043 + -1.5
r = 19.956202043 + -1.5

Combine like terms: 19.956202043 + -1.5 = 18.456202043
r = 18.456202043

Simplifying
r = 18.456202043


Subproblem 2
r + 1.5 = -19.956202043

Simplifying
r + 1.5 = -19.956202043

Reorder the terms:
1.5 + r = -19.956202043

Solving
1.5 + r = -19.956202043

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = -19.956202043 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = -19.956202043 + -1.5
r = -19.956202043 + -1.5

Combine like terms: -19.956202043 + -1.5 = -21.456202043
r = -21.456202043

Simplifying
r = -21.456202043


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {18.456202043, -21.456202043}

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