3x^2+14x-368=0

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Solution for 3x^2+14x-368=0 equation: 


Simplifying
3x2 + 14x + -368 = 0

Reorder the terms:
-368 + 14x + 3x2 = 0

Solving
-368 + 14x + 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'.
-122.6666667 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '122.6666667' to each side of the equation.
-122.6666667 + 4.666666667x + 122.6666667 + x2 = 0 + 122.6666667

Reorder the terms:
-122.6666667 + 122.6666667 + 4.666666667x + x2 = 0 + 122.6666667

Combine like terms: -122.6666667 + 122.6666667 = 0.0000000
0.0000000 + 4.666666667x + x2 = 0 + 122.6666667
4.666666667x + x2 = 0 + 122.6666667

Combine like terms: 0 + 122.6666667 = 122.6666667
4.666666667x + x2 = 122.6666667

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 122.6666667 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 122.6666667 + 5.444444448

Combine like terms: 122.6666667 + 5.444444448 = 128.111111148
5.444444448 + 4.666666667x + x2 = 128.111111148

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 128.111111148

Calculate the square root of the right side: 11.318617899

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 11.318617899 and -11.318617899.


Subproblem 1
x + 2.333333334 = 11.318617899

Simplifying
x + 2.333333334 = 11.318617899

Reorder the terms:
2.333333334 + x = 11.318617899

Solving
2.333333334 + x = 11.318617899

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 11.318617899 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 11.318617899 + -2.333333334
x = 11.318617899 + -2.333333334

Combine like terms: 11.318617899 + -2.333333334 = 8.985284565
x = 8.985284565

Simplifying
x = 8.985284565


Subproblem 2
x + 2.333333334 = -11.318617899

Simplifying
x + 2.333333334 = -11.318617899

Reorder the terms:
2.333333334 + x = -11.318617899

Solving
2.333333334 + x = -11.318617899

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -11.318617899 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -11.318617899 + -2.333333334
x = -11.318617899 + -2.333333334

Combine like terms: -11.318617899 + -2.333333334 = -13.651951233
x = -13.651951233

Simplifying
x = -13.651951233


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.985284565, -13.651951233}

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