9x^2-38x-2=0

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Solution for 9x^2-38x-2=0 equation: 


Simplifying
9x2 + -38x + -2 = 0

Reorder the terms:
-2 + -38x + 9x2 = 0

Solving
-2 + -38x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.2222222222 + -4.222222222x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -4.222222222x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -4.222222222x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -4.222222222x + x2 = 0 + 0.2222222222
-4.222222222x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-4.222222222x + x2 = 0.2222222222

The x term is -4.222222222x.  Take half its coefficient (-2.111111111).
Square it (4.456790123) and add it to both sides.

Add '4.456790123' to each side of the equation.
-4.222222222x + 4.456790123 + x2 = 0.2222222222 + 4.456790123

Reorder the terms:
4.456790123 + -4.222222222x + x2 = 0.2222222222 + 4.456790123

Combine like terms: 0.2222222222 + 4.456790123 = 4.6790123452
4.456790123 + -4.222222222x + x2 = 4.6790123452

Factor a perfect square on the left side:
(x + -2.111111111)(x + -2.111111111) = 4.6790123452

Calculate the square root of the right side: 2.163102481

Break this problem into two subproblems by setting 
(x + -2.111111111) equal to 2.163102481 and -2.163102481.


Subproblem 1
x + -2.111111111 = 2.163102481

Simplifying
x + -2.111111111 = 2.163102481

Reorder the terms:
-2.111111111 + x = 2.163102481

Solving
-2.111111111 + x = 2.163102481

Solving for variable 'x'.

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

Add '2.111111111' to each side of the equation.
-2.111111111 + 2.111111111 + x = 2.163102481 + 2.111111111

Combine like terms: -2.111111111 + 2.111111111 = 0.000000000
0.000000000 + x = 2.163102481 + 2.111111111
x = 2.163102481 + 2.111111111

Combine like terms: 2.163102481 + 2.111111111 = 4.274213592
x = 4.274213592

Simplifying
x = 4.274213592


Subproblem 2
x + -2.111111111 = -2.163102481

Simplifying
x + -2.111111111 = -2.163102481

Reorder the terms:
-2.111111111 + x = -2.163102481

Solving
-2.111111111 + x = -2.163102481

Solving for variable 'x'.

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

Add '2.111111111' to each side of the equation.
-2.111111111 + 2.111111111 + x = -2.163102481 + 2.111111111

Combine like terms: -2.111111111 + 2.111111111 = 0.000000000
0.000000000 + x = -2.163102481 + 2.111111111
x = -2.163102481 + 2.111111111

Combine like terms: -2.163102481 + 2.111111111 = -0.05199137
x = -0.05199137

Simplifying
x = -0.05199137


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.274213592, -0.05199137}

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