x(90+100x)=18

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Solution for x(90+100x)=18 equation: 


Simplifying
x(90 + 100x) = 18
(90 * x + 100x * x) = 18
(90x + 100x2) = 18

Solving
90x + 100x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 90x + 100x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 90x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 45x + 50x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 45x + 50x2)' equal to zero and attempt to solve:

Simplifying
-9 + 45x + 50x2 = 0

Solving
-9 + 45x + 50x2 = 0

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

Divide each side by '50'.
-0.18 + 0.9x + x2 = 0.0

Move the constant term to the right:

Add '0.18' to each side of the equation.
-0.18 + 0.9x + 0.18 + x2 = 0.0 + 0.18

Reorder the terms:
-0.18 + 0.18 + 0.9x + x2 = 0.0 + 0.18

Combine like terms: -0.18 + 0.18 = 0.00
0.00 + 0.9x + x2 = 0.0 + 0.18
0.9x + x2 = 0.0 + 0.18

Combine like terms: 0.0 + 0.18 = 0.18
0.9x + x2 = 0.18

The x term is 0.9x.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9x + 0.2025 + x2 = 0.18 + 0.2025

Reorder the terms:
0.2025 + 0.9x + x2 = 0.18 + 0.2025

Combine like terms: 0.18 + 0.2025 = 0.3825
0.2025 + 0.9x + x2 = 0.3825

Factor a perfect square on the left side:
(x + 0.45)(x + 0.45) = 0.3825

Calculate the square root of the right side: 0.618465844

Break this problem into two subproblems by setting 
(x + 0.45) equal to 0.618465844 and -0.618465844.


Subproblem 1
x + 0.45 = 0.618465844

Simplifying
x + 0.45 = 0.618465844

Reorder the terms:
0.45 + x = 0.618465844

Solving
0.45 + x = 0.618465844

Solving for variable 'x'.

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

Add '-0.45' to each side of the equation.
0.45 + -0.45 + x = 0.618465844 + -0.45

Combine like terms: 0.45 + -0.45 = 0.00
0.00 + x = 0.618465844 + -0.45
x = 0.618465844 + -0.45

Combine like terms: 0.618465844 + -0.45 = 0.168465844
x = 0.168465844

Simplifying
x = 0.168465844


Subproblem 2
x + 0.45 = -0.618465844

Simplifying
x + 0.45 = -0.618465844

Reorder the terms:
0.45 + x = -0.618465844

Solving
0.45 + x = -0.618465844

Solving for variable 'x'.

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

Add '-0.45' to each side of the equation.
0.45 + -0.45 + x = -0.618465844 + -0.45

Combine like terms: 0.45 + -0.45 = 0.00
0.00 + x = -0.618465844 + -0.45
x = -0.618465844 + -0.45

Combine like terms: -0.618465844 + -0.45 = -1.068465844
x = -1.068465844

Simplifying
x = -1.068465844


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.168465844, -1.068465844}
Solution
x = {0.168465844, -1.068465844}

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