(x^2)=18(0.05-x)(0.1-x)

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Solution for (x^2)=18(0.05-x)(0.1-x) equation: 


Simplifying
(x2) = 18(0.05 + -1x)(0.1 + -1x)
x2 = 18(0.05 + -1x)(0.1 + -1x)

Multiply (0.05 + -1x) * (0.1 + -1x)
x2 = 18(0.05(0.1 + -1x) + -1x * (0.1 + -1x))
x2 = 18((0.1 * 0.05 + -1x * 0.05) + -1x * (0.1 + -1x))
x2 = 18((0.005 + -0.05x) + -1x * (0.1 + -1x))
x2 = 18(0.005 + -0.05x + (0.1 * -1x + -1x * -1x))
x2 = 18(0.005 + -0.05x + (-0.1x + 1x2))

Combine like terms: -0.05x + -0.1x = -0.15x
x2 = 18(0.005 + -0.15x + 1x2)
x2 = (0.005 * 18 + -0.15x * 18 + 1x2 * 18)
x2 = (0.09 + -2.7x + 18x2)

Solving
x2 = 0.09 + -2.7x + 18x2

Solving for variable 'x'.

Reorder the terms:
-0.09 + 2.7x + x2 + -18x2 = 0.09 + -2.7x + 18x2 + -0.09 + 2.7x + -18x2

Combine like terms: x2 + -18x2 = -17x2
-0.09 + 2.7x + -17x2 = 0.09 + -2.7x + 18x2 + -0.09 + 2.7x + -18x2

Reorder the terms:
-0.09 + 2.7x + -17x2 = 0.09 + -0.09 + -2.7x + 2.7x + 18x2 + -18x2

Combine like terms: 0.09 + -0.09 = 0.00
-0.09 + 2.7x + -17x2 = 0.00 + -2.7x + 2.7x + 18x2 + -18x2
-0.09 + 2.7x + -17x2 = -2.7x + 2.7x + 18x2 + -18x2

Combine like terms: -2.7x + 2.7x = 0.0
-0.09 + 2.7x + -17x2 = 0.0 + 18x2 + -18x2
-0.09 + 2.7x + -17x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
-0.09 + 2.7x + -17x2 = 0

Begin completing the square.  Divide all terms by
-17 the coefficient of the squared term: 

Divide each side by '-17'.
0.005294117647 + -0.1588235294x + x2 = 0

Move the constant term to the right:

Add '-0.005294117647' to each side of the equation.
0.005294117647 + -0.1588235294x + -0.005294117647 + x2 = 0 + -0.005294117647

Reorder the terms:
0.005294117647 + -0.005294117647 + -0.1588235294x + x2 = 0 + -0.005294117647

Combine like terms: 0.005294117647 + -0.005294117647 = 0.000000000000
0.000000000000 + -0.1588235294x + x2 = 0 + -0.005294117647
-0.1588235294x + x2 = 0 + -0.005294117647

Combine like terms: 0 + -0.005294117647 = -0.005294117647
-0.1588235294x + x2 = -0.005294117647

The x term is -0.1588235294x.  Take half its coefficient (-0.0794117647).
Square it (0.006306228373) and add it to both sides.

Add '0.006306228373' to each side of the equation.
-0.1588235294x + 0.006306228373 + x2 = -0.005294117647 + 0.006306228373

Reorder the terms:
0.006306228373 + -0.1588235294x + x2 = -0.005294117647 + 0.006306228373

Combine like terms: -0.005294117647 + 0.006306228373 = 0.001012110726
0.006306228373 + -0.1588235294x + x2 = 0.001012110726

Factor a perfect square on the left side:
(x + -0.0794117647)(x + -0.0794117647) = 0.001012110726

Calculate the square root of the right side: 0.031813688

Break this problem into two subproblems by setting 
(x + -0.0794117647) equal to 0.031813688 and -0.031813688.


Subproblem 1
x + -0.0794117647 = 0.031813688

Simplifying
x + -0.0794117647 = 0.031813688

Reorder the terms:
-0.0794117647 + x = 0.031813688

Solving
-0.0794117647 + x = 0.031813688

Solving for variable 'x'.

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

Add '0.0794117647' to each side of the equation.
-0.0794117647 + 0.0794117647 + x = 0.031813688 + 0.0794117647

Combine like terms: -0.0794117647 + 0.0794117647 = 0.0000000000
0.0000000000 + x = 0.031813688 + 0.0794117647
x = 0.031813688 + 0.0794117647

Combine like terms: 0.031813688 + 0.0794117647 = 0.1112254527
x = 0.1112254527

Simplifying
x = 0.1112254527


Subproblem 2
x + -0.0794117647 = -0.031813688

Simplifying
x + -0.0794117647 = -0.031813688

Reorder the terms:
-0.0794117647 + x = -0.031813688

Solving
-0.0794117647 + x = -0.031813688

Solving for variable 'x'.

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

Add '0.0794117647' to each side of the equation.
-0.0794117647 + 0.0794117647 + x = -0.031813688 + 0.0794117647

Combine like terms: -0.0794117647 + 0.0794117647 = 0.0000000000
0.0000000000 + x = -0.031813688 + 0.0794117647
x = -0.031813688 + 0.0794117647

Combine like terms: -0.031813688 + 0.0794117647 = 0.0475980767
x = 0.0475980767

Simplifying
x = 0.0475980767


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1112254527, 0.0475980767}

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