3x^2-20x-9=0

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Solution for 3x^2-20x-9=0 equation: 


Simplifying
3x2 + -20x + -9 = 0

Reorder the terms:
-9 + -20x + 3x2 = 0

Solving
-9 + -20x + 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 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -6.666666667x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -6.666666667x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -6.666666667x + x2 = 0 + 3
-6.666666667x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-6.666666667x + x2 = 3

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 3 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 3 + 11.11111112

Combine like terms: 3 + 11.11111112 = 14.11111112
11.11111112 + -6.666666667x + x2 = 14.11111112

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 14.11111112

Calculate the square root of the right side: 3.756475891

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 3.756475891 and -3.756475891.


Subproblem 1
x + -3.333333334 = 3.756475891

Simplifying
x + -3.333333334 = 3.756475891

Reorder the terms:
-3.333333334 + x = 3.756475891

Solving
-3.333333334 + x = 3.756475891

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 3.756475891 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 3.756475891 + 3.333333334
x = 3.756475891 + 3.333333334

Combine like terms: 3.756475891 + 3.333333334 = 7.089809225
x = 7.089809225

Simplifying
x = 7.089809225


Subproblem 2
x + -3.333333334 = -3.756475891

Simplifying
x + -3.333333334 = -3.756475891

Reorder the terms:
-3.333333334 + x = -3.756475891

Solving
-3.333333334 + x = -3.756475891

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -3.756475891 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -3.756475891 + 3.333333334
x = -3.756475891 + 3.333333334

Combine like terms: -3.756475891 + 3.333333334 = -0.423142557
x = -0.423142557

Simplifying
x = -0.423142557


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.089809225, -0.423142557}

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