3x^2+56x+28=0

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Solution for 3x^2+56x+28=0 equation: 


Simplifying
3x2 + 56x + 28 = 0

Reorder the terms:
28 + 56x + 3x2 = 0

Solving
28 + 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'.
9.333333333 + 18.66666667x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + 18.66666667x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + 18.66666667x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + 18.66666667x + x2 = 0 + -9.333333333
18.66666667x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
18.66666667x + x2 = -9.333333333

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 = -9.333333333 + 87.11111114

Reorder the terms:
87.11111114 + 18.66666667x + x2 = -9.333333333 + 87.11111114

Combine like terms: -9.333333333 + 87.11111114 = 77.777777807
87.11111114 + 18.66666667x + x2 = 77.777777807

Factor a perfect square on the left side:
(x + 9.333333335)(x + 9.333333335) = 77.777777807

Calculate the square root of the right side: 8.819171039

Break this problem into two subproblems by setting 
(x + 9.333333335) equal to 8.819171039 and -8.819171039.


Subproblem 1
x + 9.333333335 = 8.819171039

Simplifying
x + 9.333333335 = 8.819171039

Reorder the terms:
9.333333335 + x = 8.819171039

Solving
9.333333335 + x = 8.819171039

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 = 8.819171039 + -9.333333335

Combine like terms: 9.333333335 + -9.333333335 = 0.000000000
0.000000000 + x = 8.819171039 + -9.333333335
x = 8.819171039 + -9.333333335

Combine like terms: 8.819171039 + -9.333333335 = -0.514162296
x = -0.514162296

Simplifying
x = -0.514162296


Subproblem 2
x + 9.333333335 = -8.819171039

Simplifying
x + 9.333333335 = -8.819171039

Reorder the terms:
9.333333335 + x = -8.819171039

Solving
9.333333335 + x = -8.819171039

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 = -8.819171039 + -9.333333335

Combine like terms: 9.333333335 + -9.333333335 = 0.000000000
0.000000000 + x = -8.819171039 + -9.333333335
x = -8.819171039 + -9.333333335

Combine like terms: -8.819171039 + -9.333333335 = -18.152504374
x = -18.152504374

Simplifying
x = -18.152504374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.514162296, -18.152504374}

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