9x^2-4x-2=0

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Solution for 9x^2-4x-2=0 equation: 


Simplifying
9x2 + -4x + -2 = 0

Reorder the terms:
-2 + -4x + 9x2 = 0

Solving
-2 + -4x + 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 + -0.4444444444x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -0.4444444444x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -0.4444444444x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -0.4444444444x + x2 = 0 + 0.2222222222
-0.4444444444x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-0.4444444444x + x2 = 0.2222222222

The x term is -0.4444444444x.  Take half its coefficient (-0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
-0.4444444444x + 0.04938271604 + x2 = 0.2222222222 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444x + x2 = 0.2222222222 + 0.04938271604

Combine like terms: 0.2222222222 + 0.04938271604 = 0.27160493824
0.04938271604 + -0.4444444444x + x2 = 0.27160493824

Factor a perfect square on the left side:
(x + -0.2222222222)(x + -0.2222222222) = 0.27160493824

Calculate the square root of the right side: 0.521157307

Break this problem into two subproblems by setting 
(x + -0.2222222222) equal to 0.521157307 and -0.521157307.


Subproblem 1
x + -0.2222222222 = 0.521157307

Simplifying
x + -0.2222222222 = 0.521157307

Reorder the terms:
-0.2222222222 + x = 0.521157307

Solving
-0.2222222222 + x = 0.521157307

Solving for variable 'x'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + x = 0.521157307 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x = 0.521157307 + 0.2222222222
x = 0.521157307 + 0.2222222222

Combine like terms: 0.521157307 + 0.2222222222 = 0.7433795292
x = 0.7433795292

Simplifying
x = 0.7433795292


Subproblem 2
x + -0.2222222222 = -0.521157307

Simplifying
x + -0.2222222222 = -0.521157307

Reorder the terms:
-0.2222222222 + x = -0.521157307

Solving
-0.2222222222 + x = -0.521157307

Solving for variable 'x'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + x = -0.521157307 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x = -0.521157307 + 0.2222222222
x = -0.521157307 + 0.2222222222

Combine like terms: -0.521157307 + 0.2222222222 = -0.2989350848
x = -0.2989350848

Simplifying
x = -0.2989350848


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7433795292, -0.2989350848}

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