3x^2-6x+1=0

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Solution for 3x^2-6x+1=0 equation:


Simplifying
3x2 + -6x + 1 = 0

Reorder the terms:
1 + -6x + 3x2 = 0

Solving
1 + -6x + 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'.
0.3333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -2x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -2x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.3333333333
-2x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-2x + x2 = -0.3333333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.3333333333 + 1

Reorder the terms:
1 + -2x + x2 = -0.3333333333 + 1

Combine like terms: -0.3333333333 + 1 = 0.6666666667
1 + -2x + x2 = 0.6666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.6666666667

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(x + -1) equal to 0.816496581 and -0.816496581.

Subproblem 1

x + -1 = 0.816496581 Simplifying x + -1 = 0.816496581 Reorder the terms: -1 + x = 0.816496581 Solving -1 + x = 0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.816496581 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.816496581 + 1 x = 0.816496581 + 1 Combine like terms: 0.816496581 + 1 = 1.816496581 x = 1.816496581 Simplifying x = 1.816496581

Subproblem 2

x + -1 = -0.816496581 Simplifying x + -1 = -0.816496581 Reorder the terms: -1 + x = -0.816496581 Solving -1 + x = -0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.816496581 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.816496581 + 1 x = -0.816496581 + 1 Combine like terms: -0.816496581 + 1 = 0.183503419 x = 0.183503419 Simplifying x = 0.183503419

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.816496581, 0.183503419}

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