3x^2+32x+14=0

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Solution for 3x^2+32x+14=0 equation: 


Simplifying
3x2 + 32x + 14 = 0

Reorder the terms:
14 + 32x + 3x2 = 0

Solving
14 + 32x + 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'.
4.666666667 + 10.66666667x + x2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + 10.66666667x + -4.666666667 + x2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + 10.66666667x + x2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + 10.66666667x + x2 = 0 + -4.666666667
10.66666667x + x2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
10.66666667x + x2 = -4.666666667

The x term is 10.66666667x.  Take half its coefficient (5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
10.66666667x + 28.44444446 + x2 = -4.666666667 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667x + x2 = -4.666666667 + 28.44444446

Combine like terms: -4.666666667 + 28.44444446 = 23.777777793
28.44444446 + 10.66666667x + x2 = 23.777777793

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = 23.777777793

Calculate the square root of the right side: 4.876246281

Break this problem into two subproblems by setting 
(x + 5.333333335) equal to 4.876246281 and -4.876246281.


Subproblem 1
x + 5.333333335 = 4.876246281

Simplifying
x + 5.333333335 = 4.876246281

Reorder the terms:
5.333333335 + x = 4.876246281

Solving
5.333333335 + x = 4.876246281

Solving for variable 'x'.

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

Add '-5.333333335' to each side of the equation.
5.333333335 + -5.333333335 + x = 4.876246281 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = 4.876246281 + -5.333333335
x = 4.876246281 + -5.333333335

Combine like terms: 4.876246281 + -5.333333335 = -0.457087054
x = -0.457087054

Simplifying
x = -0.457087054


Subproblem 2
x + 5.333333335 = -4.876246281

Simplifying
x + 5.333333335 = -4.876246281

Reorder the terms:
5.333333335 + x = -4.876246281

Solving
5.333333335 + x = -4.876246281

Solving for variable 'x'.

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

Add '-5.333333335' to each side of the equation.
5.333333335 + -5.333333335 + x = -4.876246281 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = -4.876246281 + -5.333333335
x = -4.876246281 + -5.333333335

Combine like terms: -4.876246281 + -5.333333335 = -10.209579616
x = -10.209579616

Simplifying
x = -10.209579616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.457087054, -10.209579616}

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