3x^2-2x-12=0

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Solution for 3x^2-2x-12=0 equation:


Simplifying
3x2 + -2x + -12 = 0

Reorder the terms:
-12 + -2x + 3x2 = 0

Solving
-12 + -2x + 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'.
-4 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -0.6666666667x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -0.6666666667x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -0.6666666667x + x2 = 0 + 4
-0.6666666667x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-0.6666666667x + x2 = 4

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 4 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 4 + 0.1111111112

Combine like terms: 4 + 0.1111111112 = 4.1111111112
0.1111111112 + -0.6666666667x + x2 = 4.1111111112

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 4.1111111112

Calculate the square root of the right side: 2.02758751

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 2.02758751 and -2.02758751.

Subproblem 1

x + -0.3333333334 = 2.02758751 Simplifying x + -0.3333333334 = 2.02758751 Reorder the terms: -0.3333333334 + x = 2.02758751 Solving -0.3333333334 + x = 2.02758751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 2.02758751 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.02758751 + 0.3333333334 x = 2.02758751 + 0.3333333334 Combine like terms: 2.02758751 + 0.3333333334 = 2.3609208434 x = 2.3609208434 Simplifying x = 2.3609208434

Subproblem 2

x + -0.3333333334 = -2.02758751 Simplifying x + -0.3333333334 = -2.02758751 Reorder the terms: -0.3333333334 + x = -2.02758751 Solving -0.3333333334 + x = -2.02758751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -2.02758751 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.02758751 + 0.3333333334 x = -2.02758751 + 0.3333333334 Combine like terms: -2.02758751 + 0.3333333334 = -1.6942541766 x = -1.6942541766 Simplifying x = -1.6942541766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.3609208434, -1.6942541766}

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