9a^2+48a+32=0

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Solution for 9a^2+48a+32=0 equation: 


Simplifying
9a2 + 48a + 32 = 0

Reorder the terms:
32 + 48a + 9a2 = 0

Solving
32 + 48a + 9a2 = 0

Solving for variable 'a'.

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

Divide each side by '9'.
3.555555556 + 5.333333333a + a2 = 0

Move the constant term to the right:

Add '-3.555555556' to each side of the equation.
3.555555556 + 5.333333333a + -3.555555556 + a2 = 0 + -3.555555556

Reorder the terms:
3.555555556 + -3.555555556 + 5.333333333a + a2 = 0 + -3.555555556

Combine like terms: 3.555555556 + -3.555555556 = 0.000000000
0.000000000 + 5.333333333a + a2 = 0 + -3.555555556
5.333333333a + a2 = 0 + -3.555555556

Combine like terms: 0 + -3.555555556 = -3.555555556
5.333333333a + a2 = -3.555555556

The a term is 5.333333333a.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333a + 7.111111113 + a2 = -3.555555556 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333a + a2 = -3.555555556 + 7.111111113

Combine like terms: -3.555555556 + 7.111111113 = 3.555555557
7.111111113 + 5.333333333a + a2 = 3.555555557

Factor a perfect square on the left side:
(a + 2.666666667)(a + 2.666666667) = 3.555555557

Calculate the square root of the right side: 1.885618084

Break this problem into two subproblems by setting 
(a + 2.666666667) equal to 1.885618084 and -1.885618084.


Subproblem 1
a + 2.666666667 = 1.885618084

Simplifying
a + 2.666666667 = 1.885618084

Reorder the terms:
2.666666667 + a = 1.885618084

Solving
2.666666667 + a = 1.885618084

Solving for variable 'a'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + a = 1.885618084 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + a = 1.885618084 + -2.666666667
a = 1.885618084 + -2.666666667

Combine like terms: 1.885618084 + -2.666666667 = -0.781048583
a = -0.781048583

Simplifying
a = -0.781048583


Subproblem 2
a + 2.666666667 = -1.885618084

Simplifying
a + 2.666666667 = -1.885618084

Reorder the terms:
2.666666667 + a = -1.885618084

Solving
2.666666667 + a = -1.885618084

Solving for variable 'a'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + a = -1.885618084 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + a = -1.885618084 + -2.666666667
a = -1.885618084 + -2.666666667

Combine like terms: -1.885618084 + -2.666666667 = -4.552284751
a = -4.552284751

Simplifying
a = -4.552284751


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.781048583, -4.552284751}

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