(3x^2)-14x-3=0

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Solution for (3x^2)-14x-3=0 equation: 


Simplifying
(3x2) + -14x + -3 = 0

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

Solving
-3 + -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'.
-1 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4.666666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4.666666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4.666666667x + x2 = 0 + 1
-4.666666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4.666666667x + x2 = 1

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 = 1 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 1 + 5.444444448

Combine like terms: 1 + 5.444444448 = 6.444444448
5.444444448 + -4.666666667x + x2 = 6.444444448

Factor a perfect square on the left side:
((x) + -2.333333334)((x) + -2.333333334) = 6.444444448

Calculate the square root of the right side: 2.538591036

Break this problem into two subproblems by setting 
((x) + -2.333333334) equal to 2.538591036 and -2.538591036.


Subproblem 1
(x) + -2.333333334 = 2.538591036

Simplifying
(x) + -2.333333334 = 2.538591036
x + -2.333333334 = 2.538591036

Reorder the terms:
-2.333333334 + x = 2.538591036

Solving
-2.333333334 + x = 2.538591036

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 = 2.538591036 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 2.538591036 + 2.333333334
x = 2.538591036 + 2.333333334

Combine like terms: 2.538591036 + 2.333333334 = 4.87192437
x = 4.87192437

Simplifying
x = 4.87192437


Subproblem 2
(x) + -2.333333334 = -2.538591036

Simplifying
(x) + -2.333333334 = -2.538591036
x + -2.333333334 = -2.538591036

Reorder the terms:
-2.333333334 + x = -2.538591036

Solving
-2.333333334 + x = -2.538591036

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 = -2.538591036 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -2.538591036 + 2.333333334
x = -2.538591036 + 2.333333334

Combine like terms: -2.538591036 + 2.333333334 = -0.205257702
x = -0.205257702

Simplifying
x = -0.205257702


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.87192437, -0.205257702}

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