4x^2+6x-2=x^2-2x+2

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Solution for 4x^2+6x-2=x^2-2x+2 equation: 


Simplifying
4x2 + 6x + -2 = x2 + -2x + 2

Reorder the terms:
-2 + 6x + 4x2 = x2 + -2x + 2

Reorder the terms:
-2 + 6x + 4x2 = 2 + -2x + x2

Solving
-2 + 6x + 4x2 = 2 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-2 + -2 + 6x + 2x + 4x2 + -1x2 = 2 + -2x + x2 + -2 + 2x + -1x2

Combine like terms: -2 + -2 = -4
-4 + 6x + 2x + 4x2 + -1x2 = 2 + -2x + x2 + -2 + 2x + -1x2

Combine like terms: 6x + 2x = 8x
-4 + 8x + 4x2 + -1x2 = 2 + -2x + x2 + -2 + 2x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-4 + 8x + 3x2 = 2 + -2x + x2 + -2 + 2x + -1x2

Reorder the terms:
-4 + 8x + 3x2 = 2 + -2 + -2x + 2x + x2 + -1x2

Combine like terms: 2 + -2 = 0
-4 + 8x + 3x2 = 0 + -2x + 2x + x2 + -1x2
-4 + 8x + 3x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-4 + 8x + 3x2 = 0 + x2 + -1x2
-4 + 8x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 8x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 2.666666667x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 2.666666667x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + 1.333333333
2.666666667x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
2.666666667x + x2 = 1.333333333

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 = 1.333333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 1.333333333 + 1.777777780

Combine like terms: 1.333333333 + 1.777777780 = 3.111111113
1.777777780 + 2.666666667x + x2 = 3.111111113

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 3.111111113

Calculate the square root of the right side: 1.763834208

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 1.763834208 and -1.763834208.


Subproblem 1
x + 1.333333334 = 1.763834208

Simplifying
x + 1.333333334 = 1.763834208

Reorder the terms:
1.333333334 + x = 1.763834208

Solving
1.333333334 + x = 1.763834208

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 = 1.763834208 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 1.763834208 + -1.333333334
x = 1.763834208 + -1.333333334

Combine like terms: 1.763834208 + -1.333333334 = 0.430500874
x = 0.430500874

Simplifying
x = 0.430500874


Subproblem 2
x + 1.333333334 = -1.763834208

Simplifying
x + 1.333333334 = -1.763834208

Reorder the terms:
1.333333334 + x = -1.763834208

Solving
1.333333334 + x = -1.763834208

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 = -1.763834208 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -1.763834208 + -1.333333334
x = -1.763834208 + -1.333333334

Combine like terms: -1.763834208 + -1.333333334 = -3.097167542
x = -3.097167542

Simplifying
x = -3.097167542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.430500874, -3.097167542}

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