9r^2+12r+36=0

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Solution for 9r^2+12r+36=0 equation: 


Simplifying
9r2 + 12r + 36 = 0

Reorder the terms:
36 + 12r + 9r2 = 0

Solving
36 + 12r + 9r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 4r + 3r2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(12 + 4r + 3r2)' equal to zero and attempt to solve:

Simplifying
12 + 4r + 3r2 = 0

Solving
12 + 4r + 3r2 = 0

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

Divide each side by '3'.
4 + 1.333333333r + r2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 1.333333333r + -4 + r2 = 0 + -4

Reorder the terms:
4 + -4 + 1.333333333r + r2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 1.333333333r + r2 = 0 + -4
1.333333333r + r2 = 0 + -4

Combine like terms: 0 + -4 = -4
1.333333333r + r2 = -4

The r term is 1.333333333r.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333r + 0.4444444442 + r2 = -4 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333r + r2 = -4 + 0.4444444442

Combine like terms: -4 + 0.4444444442 = -3.5555555558
0.4444444442 + 1.333333333r + r2 = -3.5555555558

Factor a perfect square on the left side:
(r + 0.6666666665)(r + 0.6666666665) = -3.5555555558

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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