9x^2+3x-11-2=3x^2-4x-1(27x-9)

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Solution for 9x^2+3x-11-2=3x^2-4x-1(27x-9) equation: 


Simplifying
9x2 + 3x + -11 + -2 = 3x2 + -4x + -1(27x + -9)

Reorder the terms:
-11 + -2 + 3x + 9x2 = 3x2 + -4x + -1(27x + -9)

Combine like terms: -11 + -2 = -13
-13 + 3x + 9x2 = 3x2 + -4x + -1(27x + -9)

Reorder the terms:
-13 + 3x + 9x2 = 3x2 + -4x + -1(-9 + 27x)
-13 + 3x + 9x2 = 3x2 + -4x + (-9 * -1 + 27x * -1)
-13 + 3x + 9x2 = 3x2 + -4x + (9 + -27x)

Reorder the terms:
-13 + 3x + 9x2 = 9 + -4x + -27x + 3x2

Combine like terms: -4x + -27x = -31x
-13 + 3x + 9x2 = 9 + -31x + 3x2

Solving
-13 + 3x + 9x2 = 9 + -31x + 3x2

Solving for variable 'x'.

Reorder the terms:
-13 + -9 + 3x + 31x + 9x2 + -3x2 = 9 + -31x + 3x2 + -9 + 31x + -3x2

Combine like terms: -13 + -9 = -22
-22 + 3x + 31x + 9x2 + -3x2 = 9 + -31x + 3x2 + -9 + 31x + -3x2

Combine like terms: 3x + 31x = 34x
-22 + 34x + 9x2 + -3x2 = 9 + -31x + 3x2 + -9 + 31x + -3x2

Combine like terms: 9x2 + -3x2 = 6x2
-22 + 34x + 6x2 = 9 + -31x + 3x2 + -9 + 31x + -3x2

Reorder the terms:
-22 + 34x + 6x2 = 9 + -9 + -31x + 31x + 3x2 + -3x2

Combine like terms: 9 + -9 = 0
-22 + 34x + 6x2 = 0 + -31x + 31x + 3x2 + -3x2
-22 + 34x + 6x2 = -31x + 31x + 3x2 + -3x2

Combine like terms: -31x + 31x = 0
-22 + 34x + 6x2 = 0 + 3x2 + -3x2
-22 + 34x + 6x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-22 + 34x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 17x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + 17x + 3x2)' equal to zero and attempt to solve:

Simplifying
-11 + 17x + 3x2 = 0

Solving
-11 + 17x + 3x2 = 0

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

Divide each side by '3'.
-3.666666667 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + 5.666666667x + 3.666666667 + x2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + 5.666666667x + x2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + 5.666666667x + x2 = 0 + 3.666666667
5.666666667x + x2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
5.666666667x + x2 = 3.666666667

The x term is 5.666666667x.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667x + 8.027777782 + x2 = 3.666666667 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = 3.666666667 + 8.027777782

Combine like terms: 3.666666667 + 8.027777782 = 11.694444449
8.027777782 + 5.666666667x + x2 = 11.694444449

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 11.694444449

Calculate the square root of the right side: 3.419714089

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 3.419714089 and -3.419714089.


Subproblem 1
x + 2.833333334 = 3.419714089

Simplifying
x + 2.833333334 = 3.419714089

Reorder the terms:
2.833333334 + x = 3.419714089

Solving
2.833333334 + x = 3.419714089

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = 3.419714089 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 3.419714089 + -2.833333334
x = 3.419714089 + -2.833333334

Combine like terms: 3.419714089 + -2.833333334 = 0.586380755
x = 0.586380755

Simplifying
x = 0.586380755


Subproblem 2
x + 2.833333334 = -3.419714089

Simplifying
x + 2.833333334 = -3.419714089

Reorder the terms:
2.833333334 + x = -3.419714089

Solving
2.833333334 + x = -3.419714089

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = -3.419714089 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -3.419714089 + -2.833333334
x = -3.419714089 + -2.833333334

Combine like terms: -3.419714089 + -2.833333334 = -6.253047423
x = -6.253047423

Simplifying
x = -6.253047423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.586380755, -6.253047423}
Solution
x = {0.586380755, -6.253047423}

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