3x^2+-6x-2=3

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


Simplifying
3x2 + -6x + -2 = 3

Reorder the terms:
-2 + -6x + 3x2 = 3

Solving
-2 + -6x + 3x2 = 3

Solving for variable 'x'.

Reorder the terms:
-2 + -3 + -6x + 3x2 = 3 + -3

Combine like terms: -2 + -3 = -5
-5 + -6x + 3x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-5 + -6x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + -2x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -2x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -2x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -2x + x2 = 0 + 1.666666667
-2x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-2x + x2 = 1.666666667

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 = 1.666666667 + 1

Reorder the terms:
1 + -2x + x2 = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
1 + -2x + x2 = 2.666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(x + -1) equal to 1.632993162 and -1.632993162.

Subproblem 1

x + -1 = 1.632993162 Simplifying x + -1 = 1.632993162 Reorder the terms: -1 + x = 1.632993162 Solving -1 + x = 1.632993162 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 = 1.632993162 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.632993162 + 1 x = 1.632993162 + 1 Combine like terms: 1.632993162 + 1 = 2.632993162 x = 2.632993162 Simplifying x = 2.632993162

Subproblem 2

x + -1 = -1.632993162 Simplifying x + -1 = -1.632993162 Reorder the terms: -1 + x = -1.632993162 Solving -1 + x = -1.632993162 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 = -1.632993162 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.632993162 + 1 x = -1.632993162 + 1 Combine like terms: -1.632993162 + 1 = -0.632993162 x = -0.632993162 Simplifying x = -0.632993162

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.632993162, -0.632993162}

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