3x^2+24x+32=0

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Solution for 3x^2+24x+32=0 equation: 


Simplifying
3x2 + 24x + 32 = 0

Reorder the terms:
32 + 24x + 3x2 = 0

Solving
32 + 24x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
10.66666667 + 8x + x2 = 0

Move the constant term to the right:

Add '-10.66666667' to each side of the equation.
10.66666667 + 8x + -10.66666667 + x2 = 0 + -10.66666667

Reorder the terms:
10.66666667 + -10.66666667 + 8x + x2 = 0 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + 8x + x2 = 0 + -10.66666667
8x + x2 = 0 + -10.66666667

Combine like terms: 0 + -10.66666667 = -10.66666667
8x + x2 = -10.66666667

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -10.66666667 + 16

Reorder the terms:
16 + 8x + x2 = -10.66666667 + 16

Combine like terms: -10.66666667 + 16 = 5.33333333
16 + 8x + x2 = 5.33333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = 5.33333333

Calculate the square root of the right side: 2.309401076

Break this problem into two subproblems by setting 
(x + 4) equal to 2.309401076 and -2.309401076.


Subproblem 1
x + 4 = 2.309401076

Simplifying
x + 4 = 2.309401076

Reorder the terms:
4 + x = 2.309401076

Solving
4 + x = 2.309401076

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 2.309401076 + -4

Combine like terms: 4 + -4 = 0
0 + x = 2.309401076 + -4
x = 2.309401076 + -4

Combine like terms: 2.309401076 + -4 = -1.690598924
x = -1.690598924

Simplifying
x = -1.690598924


Subproblem 2
x + 4 = -2.309401076

Simplifying
x + 4 = -2.309401076

Reorder the terms:
4 + x = -2.309401076

Solving
4 + x = -2.309401076

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -2.309401076 + -4

Combine like terms: 4 + -4 = 0
0 + x = -2.309401076 + -4
x = -2.309401076 + -4

Combine like terms: -2.309401076 + -4 = -6.309401076
x = -6.309401076

Simplifying
x = -6.309401076


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.690598924, -6.309401076}

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