3x^2+14x-6=0

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Solution for 3x^2+14x-6=0 equation: 


Simplifying
3x2 + 14x + -6 = 0

Reorder the terms:
-6 + 14x + 3x2 = 0

Solving
-6 + 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'.
-2 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4.666666667x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 4.666666667x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4.666666667x + x2 = 0 + 2
4.666666667x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
4.666666667x + x2 = 2

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 = 2 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 2 + 5.444444448

Combine like terms: 2 + 5.444444448 = 7.444444448
5.444444448 + 4.666666667x + x2 = 7.444444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 7.444444448

Calculate the square root of the right side: 2.728450925

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 2.728450925 and -2.728450925.


Subproblem 1
x + 2.333333334 = 2.728450925

Simplifying
x + 2.333333334 = 2.728450925

Reorder the terms:
2.333333334 + x = 2.728450925

Solving
2.333333334 + x = 2.728450925

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 = 2.728450925 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 2.728450925 + -2.333333334
x = 2.728450925 + -2.333333334

Combine like terms: 2.728450925 + -2.333333334 = 0.395117591
x = 0.395117591

Simplifying
x = 0.395117591


Subproblem 2
x + 2.333333334 = -2.728450925

Simplifying
x + 2.333333334 = -2.728450925

Reorder the terms:
2.333333334 + x = -2.728450925

Solving
2.333333334 + x = -2.728450925

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 = -2.728450925 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -2.728450925 + -2.333333334
x = -2.728450925 + -2.333333334

Combine like terms: -2.728450925 + -2.333333334 = -5.061784259
x = -5.061784259

Simplifying
x = -5.061784259


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.395117591, -5.061784259}

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