3x^2=8x-2

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Solution for 3x^2=8x-2 equation: 


Simplifying
3x2 = 8x + -2

Reorder the terms:
3x2 = -2 + 8x

Solving
3x2 = -2 + 8x

Solving for variable 'x'.

Reorder the terms:
2 + -8x + 3x2 = -2 + 8x + 2 + -8x

Reorder the terms:
2 + -8x + 3x2 = -2 + 2 + 8x + -8x

Combine like terms: -2 + 2 = 0
2 + -8x + 3x2 = 0 + 8x + -8x
2 + -8x + 3x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
2 + -8x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -2.666666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -2.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -2.666666667x + x2 = 0 + -0.6666666667
-2.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-2.666666667x + x2 = -0.6666666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -0.6666666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -0.6666666667 + 1.777777780

Combine like terms: -0.6666666667 + 1.777777780 = 1.1111111133
1.777777780 + -2.666666667x + x2 = 1.1111111133

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 1.1111111133

Calculate the square root of the right side: 1.054092554

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 1.054092554 and -1.054092554.


Subproblem 1
x + -1.333333334 = 1.054092554

Simplifying
x + -1.333333334 = 1.054092554

Reorder the terms:
-1.333333334 + x = 1.054092554

Solving
-1.333333334 + x = 1.054092554

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 1.054092554 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 1.054092554 + 1.333333334
x = 1.054092554 + 1.333333334

Combine like terms: 1.054092554 + 1.333333334 = 2.387425888
x = 2.387425888

Simplifying
x = 2.387425888


Subproblem 2
x + -1.333333334 = -1.054092554

Simplifying
x + -1.333333334 = -1.054092554

Reorder the terms:
-1.333333334 + x = -1.054092554

Solving
-1.333333334 + x = -1.054092554

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -1.054092554 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -1.054092554 + 1.333333334
x = -1.054092554 + 1.333333334

Combine like terms: -1.054092554 + 1.333333334 = 0.27924078
x = 0.27924078

Simplifying
x = 0.27924078


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.387425888, 0.27924078}

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