0.2x(0.2x)-0.4x-0.2=0

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Solution for 0.2x(0.2x)-0.4x-0.2=0 equation:


Simplifying
0.2x(0.2x) + -0.4x + -0.2 = 0

Remove parenthesis around (0.2x)
0.2x * 0.2x + -0.4x + -0.2 = 0

Reorder the terms for easier multiplication:
0.2 * 0.2x * x + -0.4x + -0.2 = 0

Multiply 0.2 * 0.2
0.04x * x + -0.4x + -0.2 = 0

Multiply x * x
0.04x2 + -0.4x + -0.2 = 0

Reorder the terms:
-0.2 + -0.4x + 0.04x2 = 0

Solving
-0.2 + -0.4x + 0.04x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.04'.
-5 + -10x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -10x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -10x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -10x + x2 = 0 + 5
-10x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-10x + x2 = 5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 5 + 25

Reorder the terms:
25 + -10x + x2 = 5 + 25

Combine like terms: 5 + 25 = 30
25 + -10x + x2 = 30

Factor a perfect square on the left side:
(x + -5)(x + -5) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + -5) equal to 5.477225575 and -5.477225575.

Subproblem 1

x + -5 = 5.477225575 Simplifying x + -5 = 5.477225575 Reorder the terms: -5 + x = 5.477225575 Solving -5 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.477225575 + 5 x = 5.477225575 + 5 Combine like terms: 5.477225575 + 5 = 10.477225575 x = 10.477225575 Simplifying x = 10.477225575

Subproblem 2

x + -5 = -5.477225575 Simplifying x + -5 = -5.477225575 Reorder the terms: -5 + x = -5.477225575 Solving -5 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.477225575 + 5 x = -5.477225575 + 5 Combine like terms: -5.477225575 + 5 = -0.477225575 x = -0.477225575 Simplifying x = -0.477225575

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.477225575, -0.477225575}

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