3x^2-11x-1+2=0

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Solution for 3x^2-11x-1+2=0 equation: 


Simplifying
3x2 + -11x + -1 + 2 = 0

Reorder the terms:
-1 + 2 + -11x + 3x2 = 0

Combine like terms: -1 + 2 = 1
1 + -11x + 3x2 = 0

Solving
1 + -11x + 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'.
0.3333333333 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -3.666666667x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -3.666666667x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -3.666666667x + x2 = 0 + -0.3333333333
-3.666666667x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-3.666666667x + x2 = -0.3333333333

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = -0.3333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = -0.3333333333 + 3.361111114

Combine like terms: -0.3333333333 + 3.361111114 = 3.0277777807
3.361111114 + -3.666666667x + x2 = 3.0277777807

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 3.0277777807

Calculate the square root of the right side: 1.740051086

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 1.740051086 and -1.740051086.


Subproblem 1
x + -1.833333334 = 1.740051086

Simplifying
x + -1.833333334 = 1.740051086

Reorder the terms:
-1.833333334 + x = 1.740051086

Solving
-1.833333334 + x = 1.740051086

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 1.740051086 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 1.740051086 + 1.833333334
x = 1.740051086 + 1.833333334

Combine like terms: 1.740051086 + 1.833333334 = 3.57338442
x = 3.57338442

Simplifying
x = 3.57338442


Subproblem 2
x + -1.833333334 = -1.740051086

Simplifying
x + -1.833333334 = -1.740051086

Reorder the terms:
-1.833333334 + x = -1.740051086

Solving
-1.833333334 + x = -1.740051086

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -1.740051086 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -1.740051086 + 1.833333334
x = -1.740051086 + 1.833333334

Combine like terms: -1.740051086 + 1.833333334 = 0.093282248
x = 0.093282248

Simplifying
x = 0.093282248


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.57338442, 0.093282248}

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