x+x(1-x)=0.875

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Solution for x+x(1-x)=0.875 equation:


Simplifying
x + x(1 + -1x) = 0.875
x + (1 * x + -1x * x) = 0.875
x + (1x + -1x2) = 0.875

Combine like terms: x + 1x = 2x
2x + -1x2 = 0.875

Solving
2x + -1x2 = 0.875

Solving for variable 'x'.

Reorder the terms:
-0.875 + 2x + -1x2 = 0.875 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
-0.875 + 2x + -1x2 = 0.000

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
0.875 + -2x + x2 = 0.000

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + -2x + -0.875 + x2 = 0.000 + -0.875

Reorder the terms:
0.875 + -0.875 + -2x + x2 = 0.000 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + -2x + x2 = 0.000 + -0.875
-2x + x2 = 0.000 + -0.875

Combine like terms: 0.000 + -0.875 = -0.875
-2x + x2 = -0.875

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.875 + 1

Reorder the terms:
1 + -2x + x2 = -0.875 + 1

Combine like terms: -0.875 + 1 = 0.125
1 + -2x + x2 = 0.125

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(x + -1) equal to 0.353553391 and -0.353553391.

Subproblem 1

x + -1 = 0.353553391 Simplifying x + -1 = 0.353553391 Reorder the terms: -1 + x = 0.353553391 Solving -1 + x = 0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.353553391 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.353553391 + 1 x = 0.353553391 + 1 Combine like terms: 0.353553391 + 1 = 1.353553391 x = 1.353553391 Simplifying x = 1.353553391

Subproblem 2

x + -1 = -0.353553391 Simplifying x + -1 = -0.353553391 Reorder the terms: -1 + x = -0.353553391 Solving -1 + x = -0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.353553391 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.353553391 + 1 x = -0.353553391 + 1 Combine like terms: -0.353553391 + 1 = 0.646446609 x = 0.646446609 Simplifying x = 0.646446609

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.353553391, 0.646446609}

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