3x^2+40x+84=0

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Solution for 3x^2+40x+84=0 equation: 


Simplifying
3x2 + 40x + 84 = 0

Reorder the terms:
84 + 40x + 3x2 = 0

Solving
84 + 40x + 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'.
28 + 13.33333333x + x2 = 0

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + 13.33333333x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + 13.33333333x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 13.33333333x + x2 = 0 + -28
13.33333333x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
13.33333333x + x2 = -28

The x term is 13.33333333x.  Take half its coefficient (6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
13.33333333x + 44.44444442 + x2 = -28 + 44.44444442

Reorder the terms:
44.44444442 + 13.33333333x + x2 = -28 + 44.44444442

Combine like terms: -28 + 44.44444442 = 16.44444442
44.44444442 + 13.33333333x + x2 = 16.44444442

Factor a perfect square on the left side:
(x + 6.666666665)(x + 6.666666665) = 16.44444442

Calculate the square root of the right side: 4.055175017

Break this problem into two subproblems by setting 
(x + 6.666666665) equal to 4.055175017 and -4.055175017.


Subproblem 1
x + 6.666666665 = 4.055175017

Simplifying
x + 6.666666665 = 4.055175017

Reorder the terms:
6.666666665 + x = 4.055175017

Solving
6.666666665 + x = 4.055175017

Solving for variable 'x'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + x = 4.055175017 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + x = 4.055175017 + -6.666666665
x = 4.055175017 + -6.666666665

Combine like terms: 4.055175017 + -6.666666665 = -2.611491648
x = -2.611491648

Simplifying
x = -2.611491648


Subproblem 2
x + 6.666666665 = -4.055175017

Simplifying
x + 6.666666665 = -4.055175017

Reorder the terms:
6.666666665 + x = -4.055175017

Solving
6.666666665 + x = -4.055175017

Solving for variable 'x'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + x = -4.055175017 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + x = -4.055175017 + -6.666666665
x = -4.055175017 + -6.666666665

Combine like terms: -4.055175017 + -6.666666665 = -10.721841682
x = -10.721841682

Simplifying
x = -10.721841682


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.611491648, -10.721841682}

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