(5x)(5x)-10x=9x+4

Solution for (5x)(5x)-10x=9x+4 equation:

Simplifying
(5x)(5x) + -10x = 9x + 4

Remove parenthesis around (5x)
5x(5x) + -10x = 9x + 4

Remove parenthesis around (5x)
5x * 5x + -10x = 9x + 4

Reorder the terms for easier multiplication:
5 * 5x * x + -10x = 9x + 4

Multiply 5 * 5
25x * x + -10x = 9x + 4

Multiply x * x
25x2 + -10x = 9x + 4

Reorder the terms:
-10x + 25x2 = 9x + 4

Reorder the terms:
-10x + 25x2 = 4 + 9x

Solving
-10x + 25x2 = 4 + 9x

Solving for variable 'x'.

Reorder the terms:
-4 + -10x + -9x + 25x2 = 4 + 9x + -4 + -9x

Combine like terms: -10x + -9x = -19x
-4 + -19x + 25x2 = 4 + 9x + -4 + -9x

Reorder the terms:
-4 + -19x + 25x2 = 4 + -4 + 9x + -9x

Combine like terms: 4 + -4 = 0
-4 + -19x + 25x2 = 0 + 9x + -9x
-4 + -19x + 25x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-4 + -19x + 25x2 = 0

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

Divide each side by '25'.
-0.16 + -0.76x + x2 = 0

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + -0.76x + 0.16 + x2 = 0 + 0.16

Reorder the terms:
-0.16 + 0.16 + -0.76x + x2 = 0 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + -0.76x + x2 = 0 + 0.16
-0.76x + x2 = 0 + 0.16

Combine like terms: 0 + 0.16 = 0.16
-0.76x + x2 = 0.16

The x term is -0.76x.  Take half its coefficient (-0.38).
Square it (0.1444) and add it to both sides.

Add '0.1444' to each side of the equation.
-0.76x + 0.1444 + x2 = 0.16 + 0.1444

Reorder the terms:
0.1444 + -0.76x + x2 = 0.16 + 0.1444

Combine like terms: 0.16 + 0.1444 = 0.3044
0.1444 + -0.76x + x2 = 0.3044

Factor a perfect square on the left side:
(x + -0.38)(x + -0.38) = 0.3044

Calculate the square root of the right side: 0.551724569

Break this problem into two subproblems by setting 
(x + -0.38) equal to 0.551724569 and -0.551724569.

Subproblem 1
x + -0.38 = 0.551724569

Simplifying
x + -0.38 = 0.551724569

Reorder the terms:
-0.38 + x = 0.551724569

Solving
-0.38 + x = 0.551724569

Solving for variable 'x'.

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

Add '0.38' to each side of the equation.
-0.38 + 0.38 + x = 0.551724569 + 0.38

Combine like terms: -0.38 + 0.38 = 0.00
0.00 + x = 0.551724569 + 0.38
x = 0.551724569 + 0.38

Combine like terms: 0.551724569 + 0.38 = 0.931724569
x = 0.931724569

Simplifying
x = 0.931724569

Subproblem 2
x + -0.38 = -0.551724569

Simplifying
x + -0.38 = -0.551724569

Reorder the terms:
-0.38 + x = -0.551724569

Solving
-0.38 + x = -0.551724569

Solving for variable 'x'.

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

Add '0.38' to each side of the equation.
-0.38 + 0.38 + x = -0.551724569 + 0.38

Combine like terms: -0.38 + 0.38 = 0.00
0.00 + x = -0.551724569 + 0.38
x = -0.551724569 + 0.38

Combine like terms: -0.551724569 + 0.38 = -0.171724569
x = -0.171724569

Simplifying
x = -0.171724569

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.931724569, -0.171724569}