10=(2x+9)200x

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Solution for 10=(2x+9)200x equation: 


Simplifying
10 = (2x + 9) * 200x

Reorder the terms:
10 = (9 + 2x) * 200x

Reorder the terms for easier multiplication:
10 = 200x(9 + 2x)
10 = (9 * 200x + 2x * 200x)
10 = (1800x + 400x2)

Solving
10 = 1800x + 400x2

Solving for variable 'x'.

Reorder the terms:
10 + -1800x + -400x2 = 1800x + -1800x + 400x2 + -400x2

Combine like terms: 1800x + -1800x = 0
10 + -1800x + -400x2 = 0 + 400x2 + -400x2
10 + -1800x + -400x2 = 400x2 + -400x2

Combine like terms: 400x2 + -400x2 = 0
10 + -1800x + -400x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + -180x + -40x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(1 + -180x + -40x2)' equal to zero and attempt to solve:

Simplifying
1 + -180x + -40x2 = 0

Solving
1 + -180x + -40x2 = 0

Begin completing the square.  Divide all terms by
-40 the coefficient of the squared term: 

Divide each side by '-40'.
-0.025 + 4.5x + x2 = 0.0

Move the constant term to the right:

Add '0.025' to each side of the equation.
-0.025 + 4.5x + 0.025 + x2 = 0.0 + 0.025

Reorder the terms:
-0.025 + 0.025 + 4.5x + x2 = 0.0 + 0.025

Combine like terms: -0.025 + 0.025 = 0.000
0.000 + 4.5x + x2 = 0.0 + 0.025
4.5x + x2 = 0.0 + 0.025

Combine like terms: 0.0 + 0.025 = 0.025
4.5x + x2 = 0.025

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 0.025 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 0.025 + 5.0625

Combine like terms: 0.025 + 5.0625 = 5.0875
5.0625 + 4.5x + x2 = 5.0875

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 5.0875

Calculate the square root of the right side: 2.255548714

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.255548714 and -2.255548714.


Subproblem 1
x + 2.25 = 2.255548714

Simplifying
x + 2.25 = 2.255548714

Reorder the terms:
2.25 + x = 2.255548714

Solving
2.25 + x = 2.255548714

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.255548714 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.255548714 + -2.25
x = 2.255548714 + -2.25

Combine like terms: 2.255548714 + -2.25 = 0.005548714
x = 0.005548714

Simplifying
x = 0.005548714


Subproblem 2
x + 2.25 = -2.255548714

Simplifying
x + 2.25 = -2.255548714

Reorder the terms:
2.25 + x = -2.255548714

Solving
2.25 + x = -2.255548714

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.255548714 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.255548714 + -2.25
x = -2.255548714 + -2.25

Combine like terms: -2.255548714 + -2.25 = -4.505548714
x = -4.505548714

Simplifying
x = -4.505548714


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.005548714, -4.505548714}
Solution
x = {0.005548714, -4.505548714}

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