3x^2+56x+16=0

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Solution for 3x^2+56x+16=0 equation: 


Simplifying
3x2 + 56x + 16 = 0

Reorder the terms:
16 + 56x + 3x2 = 0

Solving
16 + 56x + 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'.
5.333333333 + 18.66666667x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + 18.66666667x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + 18.66666667x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + 18.66666667x + x2 = 0 + -5.333333333
18.66666667x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
18.66666667x + x2 = -5.333333333

The x term is 18.66666667x.  Take half its coefficient (9.333333335).
Square it (87.11111114) and add it to both sides.

Add '87.11111114' to each side of the equation.
18.66666667x + 87.11111114 + x2 = -5.333333333 + 87.11111114

Reorder the terms:
87.11111114 + 18.66666667x + x2 = -5.333333333 + 87.11111114

Combine like terms: -5.333333333 + 87.11111114 = 81.777777807
87.11111114 + 18.66666667x + x2 = 81.777777807

Factor a perfect square on the left side:
(x + 9.333333335)(x + 9.333333335) = 81.777777807

Calculate the square root of the right side: 9.043106646

Break this problem into two subproblems by setting 
(x + 9.333333335) equal to 9.043106646 and -9.043106646.


Subproblem 1
x + 9.333333335 = 9.043106646

Simplifying
x + 9.333333335 = 9.043106646

Reorder the terms:
9.333333335 + x = 9.043106646

Solving
9.333333335 + x = 9.043106646

Solving for variable 'x'.

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

Add '-9.333333335' to each side of the equation.
9.333333335 + -9.333333335 + x = 9.043106646 + -9.333333335

Combine like terms: 9.333333335 + -9.333333335 = 0.000000000
0.000000000 + x = 9.043106646 + -9.333333335
x = 9.043106646 + -9.333333335

Combine like terms: 9.043106646 + -9.333333335 = -0.290226689
x = -0.290226689

Simplifying
x = -0.290226689


Subproblem 2
x + 9.333333335 = -9.043106646

Simplifying
x + 9.333333335 = -9.043106646

Reorder the terms:
9.333333335 + x = -9.043106646

Solving
9.333333335 + x = -9.043106646

Solving for variable 'x'.

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

Add '-9.333333335' to each side of the equation.
9.333333335 + -9.333333335 + x = -9.043106646 + -9.333333335

Combine like terms: 9.333333335 + -9.333333335 = 0.000000000
0.000000000 + x = -9.043106646 + -9.333333335
x = -9.043106646 + -9.333333335

Combine like terms: -9.043106646 + -9.333333335 = -18.376439981
x = -18.376439981

Simplifying
x = -18.376439981


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.290226689, -18.376439981}

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