3x^2=14x+2

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


Simplifying
3x2 = 14x + 2

Reorder the terms:
3x2 = 2 + 14x

Solving
3x2 = 2 + 14x

Solving for variable 'x'.

Reorder the terms:
-2 + -14x + 3x2 = 2 + 14x + -2 + -14x

Reorder the terms:
-2 + -14x + 3x2 = 2 + -2 + 14x + -14x

Combine like terms: 2 + -2 = 0
-2 + -14x + 3x2 = 0 + 14x + -14x
-2 + -14x + 3x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-2 + -14x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-0.6666666667 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -4.666666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -4.666666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -4.666666667x + x2 = 0 + 0.6666666667
-4.666666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-4.666666667x + x2 = 0.6666666667

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 = 0.6666666667 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 0.6666666667 + 5.444444448

Combine like terms: 0.6666666667 + 5.444444448 = 6.1111111147
5.444444448 + -4.666666667x + x2 = 6.1111111147

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 6.1111111147

Calculate the square root of the right side: 2.472066163

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.472066163 and -2.472066163.


Subproblem 1
x + -2.333333334 = 2.472066163

Simplifying
x + -2.333333334 = 2.472066163

Reorder the terms:
-2.333333334 + x = 2.472066163

Solving
-2.333333334 + x = 2.472066163

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 = 2.472066163 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 2.472066163 + 2.333333334
x = 2.472066163 + 2.333333334

Combine like terms: 2.472066163 + 2.333333334 = 4.805399497
x = 4.805399497

Simplifying
x = 4.805399497


Subproblem 2
x + -2.333333334 = -2.472066163

Simplifying
x + -2.333333334 = -2.472066163

Reorder the terms:
-2.333333334 + x = -2.472066163

Solving
-2.333333334 + x = -2.472066163

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 = -2.472066163 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -2.472066163 + 2.333333334
x = -2.472066163 + 2.333333334

Combine like terms: -2.472066163 + 2.333333334 = -0.138732829
x = -0.138732829

Simplifying
x = -0.138732829


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.805399497, -0.138732829}

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