9a^2+24a+36=0

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Solution for 9a^2+24a+36=0 equation:


Simplifying
9a2 + 24a + 36 = 0

Reorder the terms:
36 + 24a + 9a2 = 0

Solving
36 + 24a + 9a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 8a + 3a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(12 + 8a + 3a2)' equal to zero and attempt to solve:

Simplifying
12 + 8a + 3a2 = 0

Solving
12 + 8a + 3a2 = 0

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

Divide each side by '3'.
4 + 2.666666667a + a2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 2.666666667a + -4 + a2 = 0 + -4

Reorder the terms:
4 + -4 + 2.666666667a + a2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 2.666666667a + a2 = 0 + -4
2.666666667a + a2 = 0 + -4

Combine like terms: 0 + -4 = -4
2.666666667a + a2 = -4

The a term is 2.666666667a.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667a + 1.777777780 + a2 = -4 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667a + a2 = -4 + 1.777777780

Combine like terms: -4 + 1.777777780 = -2.22222222
1.777777780 + 2.666666667a + a2 = -2.22222222

Factor a perfect square on the left side:
(a + 1.333333334)(a + 1.333333334) = -2.22222222

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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