-3x^2+10x-6=0

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Solution for -3x^2+10x-6=0 equation: 


Simplifying
-3x2 + 10x + -6 = 0

Reorder the terms:
-6 + 10x + -3x2 = 0

Solving
-6 + 10x + -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'.
2 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.333333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -3.333333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.333333333x + x2 = 0 + -2
-3.333333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.333333333x + x2 = -2

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = -2 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -2 + 2.777777779

Combine like terms: -2 + 2.777777779 = 0.777777779
2.777777779 + -3.333333333x + x2 = 0.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 0.777777779

Calculate the square root of the right side: 0.881917104

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 0.881917104 and -0.881917104.


Subproblem 1
x + -1.666666667 = 0.881917104

Simplifying
x + -1.666666667 = 0.881917104

Reorder the terms:
-1.666666667 + x = 0.881917104

Solving
-1.666666667 + x = 0.881917104

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 0.881917104 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 0.881917104 + 1.666666667
x = 0.881917104 + 1.666666667

Combine like terms: 0.881917104 + 1.666666667 = 2.548583771
x = 2.548583771

Simplifying
x = 2.548583771


Subproblem 2
x + -1.666666667 = -0.881917104

Simplifying
x + -1.666666667 = -0.881917104

Reorder the terms:
-1.666666667 + x = -0.881917104

Solving
-1.666666667 + x = -0.881917104

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -0.881917104 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -0.881917104 + 1.666666667
x = -0.881917104 + 1.666666667

Combine like terms: -0.881917104 + 1.666666667 = 0.784749563
x = 0.784749563

Simplifying
x = 0.784749563


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.548583771, 0.784749563}

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