5.95x(1.4+x)=(0.2-2x)(0.2-2x)

Solution for 5.95x(1.4+x)=(0.2-2x)(0.2-2x) equation:

Simplifying
5.95x(1.4 + x) = (0.2 + -2x)(0.2 + -2x)
(1.4 * 5.95x + x * 5.95x) = (0.2 + -2x)(0.2 + -2x)
(8.33x + 5.95x2) = (0.2 + -2x)(0.2 + -2x)

Multiply (0.2 + -2x) * (0.2 + -2x)
8.33x + 5.95x2 = (0.2(0.2 + -2x) + -2x * (0.2 + -2x))
8.33x + 5.95x2 = ((0.2 * 0.2 + -2x * 0.2) + -2x * (0.2 + -2x))
8.33x + 5.95x2 = ((0.04 + -0.4x) + -2x * (0.2 + -2x))
8.33x + 5.95x2 = (0.04 + -0.4x + (0.2 * -2x + -2x * -2x))
8.33x + 5.95x2 = (0.04 + -0.4x + (-0.4x + 4x2))

Combine like terms: -0.4x + -0.4x = -0.8x
8.33x + 5.95x2 = (0.04 + -0.8x + 4x2)

Solving
8.33x + 5.95x2 = 0.04 + -0.8x + 4x2

Solving for variable 'x'.

Reorder the terms:
-0.04 + 8.33x + 0.8x + 5.95x2 + -4x2 = 0.04 + -0.8x + 4x2 + -0.04 + 0.8x + -4x2

Combine like terms: 8.33x + 0.8x = 9.13x
-0.04 + 9.13x + 5.95x2 + -4x2 = 0.04 + -0.8x + 4x2 + -0.04 + 0.8x + -4x2

Combine like terms: 5.95x2 + -4x2 = 1.95x2
-0.04 + 9.13x + 1.95x2 = 0.04 + -0.8x + 4x2 + -0.04 + 0.8x + -4x2

Reorder the terms:
-0.04 + 9.13x + 1.95x2 = 0.04 + -0.04 + -0.8x + 0.8x + 4x2 + -4x2

Combine like terms: 0.04 + -0.04 = 0.00
-0.04 + 9.13x + 1.95x2 = 0.00 + -0.8x + 0.8x + 4x2 + -4x2
-0.04 + 9.13x + 1.95x2 = -0.8x + 0.8x + 4x2 + -4x2

Combine like terms: -0.8x + 0.8x = 0.0
-0.04 + 9.13x + 1.95x2 = 0.0 + 4x2 + -4x2
-0.04 + 9.13x + 1.95x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-0.04 + 9.13x + 1.95x2 = 0

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

Divide each side by '1.95'.
-0.02051282051 + 4.682051282x + x2 = 0

Move the constant term to the right:

Add '0.02051282051' to each side of the equation.
-0.02051282051 + 4.682051282x + 0.02051282051 + x2 = 0 + 0.02051282051

Reorder the terms:
-0.02051282051 + 0.02051282051 + 4.682051282x + x2 = 0 + 0.02051282051

Combine like terms: -0.02051282051 + 0.02051282051 = 0.00000000000
0.00000000000 + 4.682051282x + x2 = 0 + 0.02051282051
4.682051282x + x2 = 0 + 0.02051282051

Combine like terms: 0 + 0.02051282051 = 0.02051282051
4.682051282x + x2 = 0.02051282051

The x term is 4.682051282x.  Take half its coefficient (2.341025641).
Square it (5.480401052) and add it to both sides.

Add '5.480401052' to each side of the equation.
4.682051282x + 5.480401052 + x2 = 0.02051282051 + 5.480401052

Reorder the terms:
5.480401052 + 4.682051282x + x2 = 0.02051282051 + 5.480401052

Combine like terms: 0.02051282051 + 5.480401052 = 5.50091387251
5.480401052 + 4.682051282x + x2 = 5.50091387251

Factor a perfect square on the left side:
(x + 2.341025641)(x + 2.341025641) = 5.50091387251

Calculate the square root of the right side: 2.34540271

Break this problem into two subproblems by setting 
(x + 2.341025641) equal to 2.34540271 and -2.34540271.

Subproblem 1
x + 2.341025641 = 2.34540271

Simplifying
x + 2.341025641 = 2.34540271

Reorder the terms:
2.341025641 + x = 2.34540271

Solving
2.341025641 + x = 2.34540271

Solving for variable 'x'.

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

Add '-2.341025641' to each side of the equation.
2.341025641 + -2.341025641 + x = 2.34540271 + -2.341025641

Combine like terms: 2.341025641 + -2.341025641 = 0.000000000
0.000000000 + x = 2.34540271 + -2.341025641
x = 2.34540271 + -2.341025641

Combine like terms: 2.34540271 + -2.341025641 = 0.004377069
x = 0.004377069

Simplifying
x = 0.004377069

Subproblem 2
x + 2.341025641 = -2.34540271

Simplifying
x + 2.341025641 = -2.34540271

Reorder the terms:
2.341025641 + x = -2.34540271

Solving
2.341025641 + x = -2.34540271

Solving for variable 'x'.

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

Add '-2.341025641' to each side of the equation.
2.341025641 + -2.341025641 + x = -2.34540271 + -2.341025641

Combine like terms: 2.341025641 + -2.341025641 = 0.000000000
0.000000000 + x = -2.34540271 + -2.341025641
x = -2.34540271 + -2.341025641

Combine like terms: -2.34540271 + -2.341025641 = -4.686428351
x = -4.686428351

Simplifying
x = -4.686428351

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.004377069, -4.686428351}