8x*8(x+4)=250

Solution for 8x*8(x+4)=250 equation:

Simplifying
8x * 8(x + 4) = 250

Reorder the terms:
8x * 8(4 + x) = 250

Reorder the terms for easier multiplication:
8 * 8x(4 + x) = 250

Multiply 8 * 8
64x(4 + x) = 250
(4 * 64x + x * 64x) = 250
(256x + 64x2) = 250

Solving
256x + 64x2 = 250

Solving for variable 'x'.

Reorder the terms:
-250 + 256x + 64x2 = 250 + -250

Combine like terms: 250 + -250 = 0
-250 + 256x + 64x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + 128x + 32x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-125 + 128x + 32x2)' equal to zero and attempt to solve:

Simplifying
-125 + 128x + 32x2 = 0

Solving
-125 + 128x + 32x2 = 0

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

Divide each side by '32'.
-3.90625 + 4x + x2 = 0

Move the constant term to the right:

Add '3.90625' to each side of the equation.
-3.90625 + 4x + 3.90625 + x2 = 0 + 3.90625

Reorder the terms:
-3.90625 + 3.90625 + 4x + x2 = 0 + 3.90625

Combine like terms: -3.90625 + 3.90625 = 0.00000
0.00000 + 4x + x2 = 0 + 3.90625
4x + x2 = 0 + 3.90625

Combine like terms: 0 + 3.90625 = 3.90625
4x + x2 = 3.90625

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 3.90625 + 4

Reorder the terms:
4 + 4x + x2 = 3.90625 + 4

Combine like terms: 3.90625 + 4 = 7.90625
4 + 4x + x2 = 7.90625

Factor a perfect square on the left side:
(x + 2)(x + 2) = 7.90625

Calculate the square root of the right side: 2.81180547

Break this problem into two subproblems by setting 
(x + 2) equal to 2.81180547 and -2.81180547.

Subproblem 1
x + 2 = 2.81180547

Simplifying
x + 2 = 2.81180547

Reorder the terms:
2 + x = 2.81180547

Solving
2 + x = 2.81180547

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.81180547 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.81180547 + -2
x = 2.81180547 + -2

Combine like terms: 2.81180547 + -2 = 0.81180547
x = 0.81180547

Simplifying
x = 0.81180547

Subproblem 2
x + 2 = -2.81180547

Simplifying
x + 2 = -2.81180547

Reorder the terms:
2 + x = -2.81180547

Solving
2 + x = -2.81180547

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.81180547 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.81180547 + -2
x = -2.81180547 + -2

Combine like terms: -2.81180547 + -2 = -4.81180547
x = -4.81180547

Simplifying
x = -4.81180547

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.81180547, -4.81180547}
Solution
x = {0.81180547, -4.81180547}