(3x-1)2=9x(x-4)-89

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Solution for (3x-1)2=9x(x-4)-89 equation: 


Simplifying
(3x + -1) * 2 = 9x(x + -4) + -89

Reorder the terms:
(-1 + 3x) * 2 = 9x(x + -4) + -89

Reorder the terms for easier multiplication:
2(-1 + 3x) = 9x(x + -4) + -89
(-1 * 2 + 3x * 2) = 9x(x + -4) + -89
(-2 + 6x) = 9x(x + -4) + -89

Reorder the terms:
-2 + 6x = 9x(-4 + x) + -89
-2 + 6x = (-4 * 9x + x * 9x) + -89
-2 + 6x = (-36x + 9x2) + -89

Reorder the terms:
-2 + 6x = -89 + -36x + 9x2

Solving
-2 + 6x = -89 + -36x + 9x2

Solving for variable 'x'.

Reorder the terms:
-2 + 89 + 6x + 36x + -9x2 = -89 + -36x + 9x2 + 89 + 36x + -9x2

Combine like terms: -2 + 89 = 87
87 + 6x + 36x + -9x2 = -89 + -36x + 9x2 + 89 + 36x + -9x2

Combine like terms: 6x + 36x = 42x
87 + 42x + -9x2 = -89 + -36x + 9x2 + 89 + 36x + -9x2

Reorder the terms:
87 + 42x + -9x2 = -89 + 89 + -36x + 36x + 9x2 + -9x2

Combine like terms: -89 + 89 = 0
87 + 42x + -9x2 = 0 + -36x + 36x + 9x2 + -9x2
87 + 42x + -9x2 = -36x + 36x + 9x2 + -9x2

Combine like terms: -36x + 36x = 0
87 + 42x + -9x2 = 0 + 9x2 + -9x2
87 + 42x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
87 + 42x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(29 + 14x + -3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(29 + 14x + -3x2)' equal to zero and attempt to solve:

Simplifying
29 + 14x + -3x2 = 0

Solving
29 + 14x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-9.666666667 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '9.666666667' to each side of the equation.
-9.666666667 + -4.666666667x + 9.666666667 + x2 = 0 + 9.666666667

Reorder the terms:
-9.666666667 + 9.666666667 + -4.666666667x + x2 = 0 + 9.666666667

Combine like terms: -9.666666667 + 9.666666667 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + 9.666666667
-4.666666667x + x2 = 0 + 9.666666667

Combine like terms: 0 + 9.666666667 = 9.666666667
-4.666666667x + x2 = 9.666666667

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 9.666666667 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 9.666666667 + 5.444444448

Combine like terms: 9.666666667 + 5.444444448 = 15.111111115
5.444444448 + -4.666666667x + x2 = 15.111111115

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 15.111111115

Calculate the square root of the right side: 3.887301264

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 3.887301264 and -3.887301264.


Subproblem 1
x + -2.333333334 = 3.887301264

Simplifying
x + -2.333333334 = 3.887301264

Reorder the terms:
-2.333333334 + x = 3.887301264

Solving
-2.333333334 + x = 3.887301264

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 3.887301264 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 3.887301264 + 2.333333334
x = 3.887301264 + 2.333333334

Combine like terms: 3.887301264 + 2.333333334 = 6.220634598
x = 6.220634598

Simplifying
x = 6.220634598


Subproblem 2
x + -2.333333334 = -3.887301264

Simplifying
x + -2.333333334 = -3.887301264

Reorder the terms:
-2.333333334 + x = -3.887301264

Solving
-2.333333334 + x = -3.887301264

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -3.887301264 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -3.887301264 + 2.333333334
x = -3.887301264 + 2.333333334

Combine like terms: -3.887301264 + 2.333333334 = -1.55396793
x = -1.55396793

Simplifying
x = -1.55396793


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.220634598, -1.55396793}
Solution
x = {6.220634598, -1.55396793}

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