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 = 1.6942541766
x = 1.6942541766

Simplifying
x = 1.6942541766


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 = -2.3609208434
x = -2.3609208434

Simplifying
x = -2.3609208434


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

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