0.4x(x-2)=0.2

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Solution for 0.4x(x-2)=0.2 equation:


Simplifying
0.4x(x + -2) = 0.2

Reorder the terms:
0.4x(-2 + x) = 0.2
(-2 * 0.4x + x * 0.4x) = 0.2
(-0.8x + 0.4x2) = 0.2

Solving
-0.8x + 0.4x2 = 0.2

Solving for variable 'x'.

Reorder the terms:
-0.2 + -0.8x + 0.4x2 = 0.2 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
-0.2 + -0.8x + 0.4x2 = 0.0

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

Divide each side by '0.4'.
-0.5 + -2x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -2x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -2x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -2x + x2 = 0 + 0.5
-2x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-2x + x2 = 0.5

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 = 0.5 + 1

Reorder the terms:
1 + -2x + x2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + -2x + x2 = 1.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + -1) equal to 1.224744871 and -1.224744871.

Subproblem 1

x + -1 = 1.224744871 Simplifying x + -1 = 1.224744871 Reorder the terms: -1 + x = 1.224744871 Solving -1 + x = 1.224744871 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 = 1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.224744871 + 1 x = 1.224744871 + 1 Combine like terms: 1.224744871 + 1 = 2.224744871 x = 2.224744871 Simplifying x = 2.224744871

Subproblem 2

x + -1 = -1.224744871 Simplifying x + -1 = -1.224744871 Reorder the terms: -1 + x = -1.224744871 Solving -1 + x = -1.224744871 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 = -1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.224744871 + 1 x = -1.224744871 + 1 Combine like terms: -1.224744871 + 1 = -0.224744871 x = -0.224744871 Simplifying x = -0.224744871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.224744871, -0.224744871}

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