-3x^2-10x+9=0

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Solution for -3x^2-10x+9=0 equation: 


Simplifying
-3x2 + -10x + 9 = 0

Reorder the terms:
9 + -10x + -3x2 = 0

Solving
9 + -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'.
-3 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 3.333333333x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 3.333333333x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3.333333333x + x2 = 0 + 3
3.333333333x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
3.333333333x + x2 = 3

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 = 3 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 3 + 2.777777779

Combine like terms: 3 + 2.777777779 = 5.777777779
2.777777779 + 3.333333333x + x2 = 5.777777779

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 5.777777779

Calculate the square root of the right side: 2.403700851

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 2.403700851 and -2.403700851.


Subproblem 1
x + 1.666666667 = 2.403700851

Simplifying
x + 1.666666667 = 2.403700851

Reorder the terms:
1.666666667 + x = 2.403700851

Solving
1.666666667 + x = 2.403700851

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 = 2.403700851 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 2.403700851 + -1.666666667
x = 2.403700851 + -1.666666667

Combine like terms: 2.403700851 + -1.666666667 = 0.737034184
x = 0.737034184

Simplifying
x = 0.737034184


Subproblem 2
x + 1.666666667 = -2.403700851

Simplifying
x + 1.666666667 = -2.403700851

Reorder the terms:
1.666666667 + x = -2.403700851

Solving
1.666666667 + x = -2.403700851

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 = -2.403700851 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -2.403700851 + -1.666666667
x = -2.403700851 + -1.666666667

Combine like terms: -2.403700851 + -1.666666667 = -4.070367518
x = -4.070367518

Simplifying
x = -4.070367518


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.737034184, -4.070367518}

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