2(1-X)(X)=0.02

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Solution for 2(1-X)(X)=0.02 equation:


Simplifying
2(1 + -1X)(X) = 0.02

Reorder the terms for easier multiplication:
2X(1 + -1X) = 0.02
(1 * 2X + -1X * 2X) = 0.02
(2X + -2X2) = 0.02

Solving
2X + -2X2 = 0.02

Solving for variable 'X'.

Reorder the terms:
-0.02 + 2X + -2X2 = 0.02 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
-0.02 + 2X + -2X2 = 0.00

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
0.01 + -1X + X2 = 0.00

Move the constant term to the right:

Add '-0.01' to each side of the equation.
0.01 + -1X + -0.01 + X2 = 0.00 + -0.01

Reorder the terms:
0.01 + -0.01 + -1X + X2 = 0.00 + -0.01

Combine like terms: 0.01 + -0.01 = 0.00
0.00 + -1X + X2 = 0.00 + -0.01
-1X + X2 = 0.00 + -0.01

Combine like terms: 0.00 + -0.01 = -0.01
-1X + X2 = -0.01

The X term is -1X.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1X + 0.25 + X2 = -0.01 + 0.25

Reorder the terms:
0.25 + -1X + X2 = -0.01 + 0.25

Combine like terms: -0.01 + 0.25 = 0.24
0.25 + -1X + X2 = 0.24

Factor a perfect square on the left side:
(X + -0.5)(X + -0.5) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(X + -0.5) equal to 0.489897949 and -0.489897949.

Subproblem 1

X + -0.5 = 0.489897949 Simplifying X + -0.5 = 0.489897949 Reorder the terms: -0.5 + X = 0.489897949 Solving -0.5 + X = 0.489897949 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = 0.489897949 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 0.489897949 + 0.5 X = 0.489897949 + 0.5 Combine like terms: 0.489897949 + 0.5 = 0.989897949 X = 0.989897949 Simplifying X = 0.989897949

Subproblem 2

X + -0.5 = -0.489897949 Simplifying X + -0.5 = -0.489897949 Reorder the terms: -0.5 + X = -0.489897949 Solving -0.5 + X = -0.489897949 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = -0.489897949 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -0.489897949 + 0.5 X = -0.489897949 + 0.5 Combine like terms: -0.489897949 + 0.5 = 0.010102051 X = 0.010102051 Simplifying X = 0.010102051

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.989897949, 0.010102051}

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