3x^2+24x+44=0

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Solution for 3x^2+24x+44=0 equation: 


Simplifying
3x2 + 24x + 44 = 0

Reorder the terms:
44 + 24x + 3x2 = 0

Solving
44 + 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'.
14.66666667 + 8x + x2 = 0

Move the constant term to the right:

Add '-14.66666667' to each side of the equation.
14.66666667 + 8x + -14.66666667 + x2 = 0 + -14.66666667

Reorder the terms:
14.66666667 + -14.66666667 + 8x + x2 = 0 + -14.66666667

Combine like terms: 14.66666667 + -14.66666667 = 0.00000000
0.00000000 + 8x + x2 = 0 + -14.66666667
8x + x2 = 0 + -14.66666667

Combine like terms: 0 + -14.66666667 = -14.66666667
8x + x2 = -14.66666667

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 = -14.66666667 + 16

Reorder the terms:
16 + 8x + x2 = -14.66666667 + 16

Combine like terms: -14.66666667 + 16 = 1.33333333
16 + 8x + x2 = 1.33333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = 1.33333333

Calculate the square root of the right side: 1.154700537

Break this problem into two subproblems by setting 
(x + 4) equal to 1.154700537 and -1.154700537.


Subproblem 1
x + 4 = 1.154700537

Simplifying
x + 4 = 1.154700537

Reorder the terms:
4 + x = 1.154700537

Solving
4 + x = 1.154700537

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 = 1.154700537 + -4

Combine like terms: 4 + -4 = 0
0 + x = 1.154700537 + -4
x = 1.154700537 + -4

Combine like terms: 1.154700537 + -4 = -2.845299463
x = -2.845299463

Simplifying
x = -2.845299463


Subproblem 2
x + 4 = -1.154700537

Simplifying
x + 4 = -1.154700537

Reorder the terms:
4 + x = -1.154700537

Solving
4 + x = -1.154700537

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 = -1.154700537 + -4

Combine like terms: 4 + -4 = 0
0 + x = -1.154700537 + -4
x = -1.154700537 + -4

Combine like terms: -1.154700537 + -4 = -5.154700537
x = -5.154700537

Simplifying
x = -5.154700537


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.845299463, -5.154700537}

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