2(x-9)2x=-2

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Solution for 2(x-9)2x=-2 equation: 


Simplifying
2(x + -9) * 2x = -2

Reorder the terms:
2(-9 + x) * 2x = -2

Reorder the terms for easier multiplication:
2 * 2x(-9 + x) = -2

Multiply 2 * 2
4x(-9 + x) = -2
(-9 * 4x + x * 4x) = -2
(-36x + 4x2) = -2

Solving
-36x + 4x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + -36x + 4x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -18x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -18x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + -18x + 2x2 = 0

Solving
1 + -18x + 2x2 = 0

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

Divide each side by '2'.
0.5 + -9x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -9x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -9x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -9x + x2 = 0 + -0.5
-9x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-9x + x2 = -0.5

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -0.5 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -0.5 + 20.25

Combine like terms: -0.5 + 20.25 = 19.75
20.25 + -9x + x2 = 19.75

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 19.75

Calculate the square root of the right side: 4.444097209

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.444097209 and -4.444097209.


Subproblem 1
x + -4.5 = 4.444097209

Simplifying
x + -4.5 = 4.444097209

Reorder the terms:
-4.5 + x = 4.444097209

Solving
-4.5 + x = 4.444097209

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.444097209 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.444097209 + 4.5
x = 4.444097209 + 4.5

Combine like terms: 4.444097209 + 4.5 = 8.944097209
x = 8.944097209

Simplifying
x = 8.944097209


Subproblem 2
x + -4.5 = -4.444097209

Simplifying
x + -4.5 = -4.444097209

Reorder the terms:
-4.5 + x = -4.444097209

Solving
-4.5 + x = -4.444097209

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.444097209 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.444097209 + 4.5
x = -4.444097209 + 4.5

Combine like terms: -4.444097209 + 4.5 = 0.055902791
x = 0.055902791

Simplifying
x = 0.055902791


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.944097209, 0.055902791}
Solution
x = {8.944097209, 0.055902791}

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