(2-3x)2+(1+4x)2=(5x-1)(5x-1)

Solution for (2-3x)2+(1+4x)2=(5x-1)(5x-1) equation:

Simplifying
(2 + -3x) * 2 + (1 + 4x) * 2 = (5x + -1)(5x + -1)

Reorder the terms for easier multiplication:
2(2 + -3x) + (1 + 4x) * 2 = (5x + -1)(5x + -1)
(2 * 2 + -3x * 2) + (1 + 4x) * 2 = (5x + -1)(5x + -1)
(4 + -6x) + (1 + 4x) * 2 = (5x + -1)(5x + -1)

Reorder the terms for easier multiplication:
4 + -6x + 2(1 + 4x) = (5x + -1)(5x + -1)
4 + -6x + (1 * 2 + 4x * 2) = (5x + -1)(5x + -1)
4 + -6x + (2 + 8x) = (5x + -1)(5x + -1)

Reorder the terms:
4 + 2 + -6x + 8x = (5x + -1)(5x + -1)

Combine like terms: 4 + 2 = 6
6 + -6x + 8x = (5x + -1)(5x + -1)

Combine like terms: -6x + 8x = 2x
6 + 2x = (5x + -1)(5x + -1)

Reorder the terms:
6 + 2x = (-1 + 5x)(5x + -1)

Reorder the terms:
6 + 2x = (-1 + 5x)(-1 + 5x)

Multiply (-1 + 5x) * (-1 + 5x)
6 + 2x = (-1(-1 + 5x) + 5x * (-1 + 5x))
6 + 2x = ((-1 * -1 + 5x * -1) + 5x * (-1 + 5x))
6 + 2x = ((1 + -5x) + 5x * (-1 + 5x))
6 + 2x = (1 + -5x + (-1 * 5x + 5x * 5x))
6 + 2x = (1 + -5x + (-5x + 25x2))

Combine like terms: -5x + -5x = -10x
6 + 2x = (1 + -10x + 25x2)

Solving
6 + 2x = 1 + -10x + 25x2

Solving for variable 'x'.

Reorder the terms:
6 + -1 + 2x + 10x + -25x2 = 1 + -10x + 25x2 + -1 + 10x + -25x2

Combine like terms: 6 + -1 = 5
5 + 2x + 10x + -25x2 = 1 + -10x + 25x2 + -1 + 10x + -25x2

Combine like terms: 2x + 10x = 12x
5 + 12x + -25x2 = 1 + -10x + 25x2 + -1 + 10x + -25x2

Reorder the terms:
5 + 12x + -25x2 = 1 + -1 + -10x + 10x + 25x2 + -25x2

Combine like terms: 1 + -1 = 0
5 + 12x + -25x2 = 0 + -10x + 10x + 25x2 + -25x2
5 + 12x + -25x2 = -10x + 10x + 25x2 + -25x2

Combine like terms: -10x + 10x = 0
5 + 12x + -25x2 = 0 + 25x2 + -25x2
5 + 12x + -25x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
5 + 12x + -25x2 = 0

Begin completing the square.  Divide all terms by
-25 the coefficient of the squared term: 

Divide each side by '-25'.
-0.2 + -0.48x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.48x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.48x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.48x + x2 = 0 + 0.2
-0.48x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-0.48x + x2 = 0.2

The x term is -0.48x.  Take half its coefficient (-0.24).
Square it (0.0576) and add it to both sides.

Add '0.0576' to each side of the equation.
-0.48x + 0.0576 + x2 = 0.2 + 0.0576

Reorder the terms:
0.0576 + -0.48x + x2 = 0.2 + 0.0576

Combine like terms: 0.2 + 0.0576 = 0.2576
0.0576 + -0.48x + x2 = 0.2576

Factor a perfect square on the left side:
(x + -0.24)(x + -0.24) = 0.2576

Calculate the square root of the right side: 0.507543102

Break this problem into two subproblems by setting 
(x + -0.24) equal to 0.507543102 and -0.507543102.

Subproblem 1
x + -0.24 = 0.507543102

Simplifying
x + -0.24 = 0.507543102

Reorder the terms:
-0.24 + x = 0.507543102

Solving
-0.24 + x = 0.507543102

Solving for variable 'x'.

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

Add '0.24' to each side of the equation.
-0.24 + 0.24 + x = 0.507543102 + 0.24

Combine like terms: -0.24 + 0.24 = 0.00
0.00 + x = 0.507543102 + 0.24
x = 0.507543102 + 0.24

Combine like terms: 0.507543102 + 0.24 = 0.747543102
x = 0.747543102

Simplifying
x = 0.747543102

Subproblem 2
x + -0.24 = -0.507543102

Simplifying
x + -0.24 = -0.507543102

Reorder the terms:
-0.24 + x = -0.507543102

Solving
-0.24 + x = -0.507543102

Solving for variable 'x'.

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

Add '0.24' to each side of the equation.
-0.24 + 0.24 + x = -0.507543102 + 0.24

Combine like terms: -0.24 + 0.24 = 0.00
0.00 + x = -0.507543102 + 0.24
x = -0.507543102 + 0.24

Combine like terms: -0.507543102 + 0.24 = -0.267543102
x = -0.267543102

Simplifying
x = -0.267543102

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.747543102, -0.267543102}