(25x^2+x+3)-(5x^2+9)=4x+1

Solution for (25x^2+x+3)-(5x^2+9)=4x+1 equation:

Simplifying
(25x2 + x + 3) + -1(5x2 + 9) = 4x + 1

Reorder the terms:
(3 + x + 25x2) + -1(5x2 + 9) = 4x + 1

Remove parenthesis around (3 + x + 25x2)
3 + x + 25x2 + -1(5x2 + 9) = 4x + 1

Reorder the terms:
3 + x + 25x2 + -1(9 + 5x2) = 4x + 1
3 + x + 25x2 + (9 * -1 + 5x2 * -1) = 4x + 1
3 + x + 25x2 + (-9 + -5x2) = 4x + 1

Reorder the terms:
3 + -9 + x + 25x2 + -5x2 = 4x + 1

Combine like terms: 3 + -9 = -6
-6 + x + 25x2 + -5x2 = 4x + 1

Combine like terms: 25x2 + -5x2 = 20x2
-6 + x + 20x2 = 4x + 1

Reorder the terms:
-6 + x + 20x2 = 1 + 4x

Solving
-6 + x + 20x2 = 1 + 4x

Solving for variable 'x'.

Reorder the terms:
-6 + -1 + x + -4x + 20x2 = 1 + 4x + -1 + -4x

Combine like terms: -6 + -1 = -7
-7 + x + -4x + 20x2 = 1 + 4x + -1 + -4x

Combine like terms: x + -4x = -3x
-7 + -3x + 20x2 = 1 + 4x + -1 + -4x

Reorder the terms:
-7 + -3x + 20x2 = 1 + -1 + 4x + -4x

Combine like terms: 1 + -1 = 0
-7 + -3x + 20x2 = 0 + 4x + -4x
-7 + -3x + 20x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-7 + -3x + 20x2 = 0

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

Divide each side by '20'.
-0.35 + -0.15x + x2 = 0.0

Move the constant term to the right:

Add '0.35' to each side of the equation.
-0.35 + -0.15x + 0.35 + x2 = 0.0 + 0.35

Reorder the terms:
-0.35 + 0.35 + -0.15x + x2 = 0.0 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + -0.15x + x2 = 0.0 + 0.35
-0.15x + x2 = 0.0 + 0.35

Combine like terms: 0.0 + 0.35 = 0.35
-0.15x + x2 = 0.35

The x term is -0.15x.  Take half its coefficient (-0.075).
Square it (0.005625) and add it to both sides.

Add '0.005625' to each side of the equation.
-0.15x + 0.005625 + x2 = 0.35 + 0.005625

Reorder the terms:
0.005625 + -0.15x + x2 = 0.35 + 0.005625

Combine like terms: 0.35 + 0.005625 = 0.355625
0.005625 + -0.15x + x2 = 0.355625

Factor a perfect square on the left side:
(x + -0.075)(x + -0.075) = 0.355625

Calculate the square root of the right side: 0.596343022

Break this problem into two subproblems by setting 
(x + -0.075) equal to 0.596343022 and -0.596343022.

Subproblem 1
x + -0.075 = 0.596343022

Simplifying
x + -0.075 = 0.596343022

Reorder the terms:
-0.075 + x = 0.596343022

Solving
-0.075 + x = 0.596343022

Solving for variable 'x'.

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

Add '0.075' to each side of the equation.
-0.075 + 0.075 + x = 0.596343022 + 0.075

Combine like terms: -0.075 + 0.075 = 0.000
0.000 + x = 0.596343022 + 0.075
x = 0.596343022 + 0.075

Combine like terms: 0.596343022 + 0.075 = 0.671343022
x = 0.671343022

Simplifying
x = 0.671343022

Subproblem 2
x + -0.075 = -0.596343022

Simplifying
x + -0.075 = -0.596343022

Reorder the terms:
-0.075 + x = -0.596343022

Solving
-0.075 + x = -0.596343022

Solving for variable 'x'.

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

Add '0.075' to each side of the equation.
-0.075 + 0.075 + x = -0.596343022 + 0.075

Combine like terms: -0.075 + 0.075 = 0.000
0.000 + x = -0.596343022 + 0.075
x = -0.596343022 + 0.075

Combine like terms: -0.596343022 + 0.075 = -0.521343022
x = -0.521343022

Simplifying
x = -0.521343022

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.671343022, -0.521343022}