(1.00-x)(0.70-x)(0.10)=0

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Solution for (1.00-x)(0.70-x)(0.10)=0 equation: 


Simplifying
(1.00 + -1x)(0.70 + -1x)(0.10) = 0

Reorder the terms for easier multiplication:
0.10(1.00 + -1x)(0.70 + -1x) = 0

Multiply (1.00 + -1x) * (0.70 + -1x)
0.10(1.00(0.70 + -1x) + -1x * (0.70 + -1x)) = 0
0.10((0.70 * 1.00 + -1x * 1.00) + -1x * (0.70 + -1x)) = 0
0.10((0.7 + -1x) + -1x * (0.70 + -1x)) = 0
0.10(0.7 + -1x + (0.70 * -1x + -1x * -1x)) = 0
0.10(0.7 + -1x + (-0.7x + 1x2)) = 0

Combine like terms: -1x + -0.7x = -1.7x
0.10(0.7 + -1.7x + 1x2) = 0
(0.7 * 0.10 + -1.7x * 0.10 + 1x2 * 0.10) = 0
(0.07 + -0.17x + 0.1x2) = 0

Solving
0.07 + -0.17x + 0.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.1'.
0.7 + -1.7x + x2 = 0

Move the constant term to the right:

Add '-0.7' to each side of the equation.
0.7 + -1.7x + -0.7 + x2 = 0 + -0.7

Reorder the terms:
0.7 + -0.7 + -1.7x + x2 = 0 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + -1.7x + x2 = 0 + -0.7
-1.7x + x2 = 0 + -0.7

Combine like terms: 0 + -0.7 = -0.7
-1.7x + x2 = -0.7

The x term is -1.7x.  Take half its coefficient (-0.85).
Square it (0.7225) and add it to both sides.

Add '0.7225' to each side of the equation.
-1.7x + 0.7225 + x2 = -0.7 + 0.7225

Reorder the terms:
0.7225 + -1.7x + x2 = -0.7 + 0.7225

Combine like terms: -0.7 + 0.7225 = 0.0225
0.7225 + -1.7x + x2 = 0.0225

Factor a perfect square on the left side:
(x + -0.85)(x + -0.85) = 0.0225

Calculate the square root of the right side: 0.15

Break this problem into two subproblems by setting 
(x + -0.85) equal to 0.15 and -0.15.


Subproblem 1
x + -0.85 = 0.15

Simplifying
x + -0.85 = 0.15

Reorder the terms:
-0.85 + x = 0.15

Solving
-0.85 + x = 0.15

Solving for variable 'x'.

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

Add '0.85' to each side of the equation.
-0.85 + 0.85 + x = 0.15 + 0.85

Combine like terms: -0.85 + 0.85 = 0.00
0.00 + x = 0.15 + 0.85
x = 0.15 + 0.85

Combine like terms: 0.15 + 0.85 = 1
x = 1

Simplifying
x = 1


Subproblem 2
x + -0.85 = -0.15

Simplifying
x + -0.85 = -0.15

Reorder the terms:
-0.85 + x = -0.15

Solving
-0.85 + x = -0.15

Solving for variable 'x'.

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

Add '0.85' to each side of the equation.
-0.85 + 0.85 + x = -0.15 + 0.85

Combine like terms: -0.85 + 0.85 = 0.00
0.00 + x = -0.15 + 0.85
x = -0.15 + 0.85

Combine like terms: -0.15 + 0.85 = 0.7
x = 0.7

Simplifying
x = 0.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1, 0.7}

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