0=3x^2-14x+12

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Solution for 0=3x^2-14x+12 equation:


Simplifying
0 = 3x2 + -14x + 12

Reorder the terms:
0 = 12 + -14x + 3x2

Solving
0 = 12 + -14x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + 14x + -3x2 = 12 + -14x + 3x2 + -12 + 14x + -3x2

Reorder the terms:
-12 + 14x + -3x2 = 12 + -12 + -14x + 14x + 3x2 + -3x2

Combine like terms: 12 + -12 = 0
-12 + 14x + -3x2 = 0 + -14x + 14x + 3x2 + -3x2
-12 + 14x + -3x2 = -14x + 14x + 3x2 + -3x2

Combine like terms: -14x + 14x = 0
-12 + 14x + -3x2 = 0 + 3x2 + -3x2
-12 + 14x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-12 + 14x + -3x2 = 0

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

Divide each side by '-3'.
4 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -4.666666667x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -4.666666667x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -4.666666667x + x2 = 0 + -4
-4.666666667x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-4.666666667x + x2 = -4

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = -4 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = -4 + 5.444444448

Combine like terms: -4 + 5.444444448 = 1.444444448
5.444444448 + -4.666666667x + x2 = 1.444444448

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 1.444444448

Calculate the square root of the right side: 1.201850427

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 1.201850427 and -1.201850427.

Subproblem 1

x + -2.333333334 = 1.201850427 Simplifying x + -2.333333334 = 1.201850427 Reorder the terms: -2.333333334 + x = 1.201850427 Solving -2.333333334 + x = 1.201850427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 1.201850427 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 1.201850427 + 2.333333334 x = 1.201850427 + 2.333333334 Combine like terms: 1.201850427 + 2.333333334 = 3.535183761 x = 3.535183761 Simplifying x = 3.535183761

Subproblem 2

x + -2.333333334 = -1.201850427 Simplifying x + -2.333333334 = -1.201850427 Reorder the terms: -2.333333334 + x = -1.201850427 Solving -2.333333334 + x = -1.201850427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -1.201850427 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -1.201850427 + 2.333333334 x = -1.201850427 + 2.333333334 Combine like terms: -1.201850427 + 2.333333334 = 1.131482907 x = 1.131482907 Simplifying x = 1.131482907

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.535183761, 1.131482907}

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