(.1-x)*(1.1-x)+.6(.15)=0

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Solution for (.1-x)*(1.1-x)+.6(.15)=0 equation: 


Simplifying
(0.1 + -1x)(1.1 + -1x) + 0.6(0.15) = 0

Multiply (0.1 + -1x) * (1.1 + -1x)
(0.1(1.1 + -1x) + -1x * (1.1 + -1x)) + 0.6(0.15) = 0
((1.1 * 0.1 + -1x * 0.1) + -1x * (1.1 + -1x)) + 0.6(0.15) = 0
((0.11 + -0.1x) + -1x * (1.1 + -1x)) + 0.6(0.15) = 0
(0.11 + -0.1x + (1.1 * -1x + -1x * -1x)) + 0.6(0.15) = 0
(0.11 + -0.1x + (-1.1x + 1x2)) + 0.6(0.15) = 0

Combine like terms: -0.1x + -1.1x = -1.2x
(0.11 + -1.2x + 1x2) + 0.6(0.15) = 0

Multiply 0.6 * 0.15
0.11 + -1.2x + 1x2 + 0.09 = 0

Reorder the terms:
0.11 + 0.09 + -1.2x + 1x2 = 0

Combine like terms: 0.11 + 0.09 = 0.2
0.2 + -1.2x + 1x2 = 0

Solving
0.2 + -1.2x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1.2x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1.2x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1.2x + x2 = 0 + -0.2
-1.2x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1.2x + x2 = -0.2

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = -0.2 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = -0.2 + 0.36

Combine like terms: -0.2 + 0.36 = 0.16
0.36 + -1.2x + x2 = 0.16

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 0.16

Calculate the square root of the right side: 0.4

Break this problem into two subproblems by setting 
(x + -0.6) equal to 0.4 and -0.4.


Subproblem 1
x + -0.6 = 0.4

Simplifying
x + -0.6 = 0.4

Reorder the terms:
-0.6 + x = 0.4

Solving
-0.6 + x = 0.4

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = 0.4 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = 0.4 + 0.6
x = 0.4 + 0.6

Combine like terms: 0.4 + 0.6 = 1
x = 1

Simplifying
x = 1


Subproblem 2
x + -0.6 = -0.4

Simplifying
x + -0.6 = -0.4

Reorder the terms:
-0.6 + x = -0.4

Solving
-0.6 + x = -0.4

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = -0.4 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = -0.4 + 0.6
x = -0.4 + 0.6

Combine like terms: -0.4 + 0.6 = 0.2
x = 0.2

Simplifying
x = 0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1, 0.2}

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