3x^2-19x+12=0

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Solution for 3x^2-19x+12=0 equation: 


Simplifying
3x2 + -19x + 12 = 0

Reorder the terms:
12 + -19x + 3x2 = 0

Solving
12 + -19x + 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 + -6.333333333x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6.333333333x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -6.333333333x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6.333333333x + x2 = 0 + -4
-6.333333333x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-6.333333333x + x2 = -4

The x term is -6.333333333x.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333x + 10.02777778 + x2 = -4 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333x + x2 = -4 + 10.02777778

Combine like terms: -4 + 10.02777778 = 6.02777778
10.02777778 + -6.333333333x + x2 = 6.02777778

Factor a perfect square on the left side:
(x + -3.166666667)(x + -3.166666667) = 6.02777778

Calculate the square root of the right side: 2.455153311

Break this problem into two subproblems by setting 
(x + -3.166666667) equal to 2.455153311 and -2.455153311.


Subproblem 1
x + -3.166666667 = 2.455153311

Simplifying
x + -3.166666667 = 2.455153311

Reorder the terms:
-3.166666667 + x = 2.455153311

Solving
-3.166666667 + x = 2.455153311

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = 2.455153311 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = 2.455153311 + 3.166666667
x = 2.455153311 + 3.166666667

Combine like terms: 2.455153311 + 3.166666667 = 5.621819978
x = 5.621819978

Simplifying
x = 5.621819978


Subproblem 2
x + -3.166666667 = -2.455153311

Simplifying
x + -3.166666667 = -2.455153311

Reorder the terms:
-3.166666667 + x = -2.455153311

Solving
-3.166666667 + x = -2.455153311

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = -2.455153311 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = -2.455153311 + 3.166666667
x = -2.455153311 + 3.166666667

Combine like terms: -2.455153311 + 3.166666667 = 0.711513356
x = 0.711513356

Simplifying
x = 0.711513356


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.621819978, 0.711513356}

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