2.56=16x^2+16x

Solution for 2.56=16x^2+16x equation:

Simplifying
2.56 = 16x2 + 16x

Reorder the terms:
2.56 = 16x + 16x2

Solving
2.56 = 16x + 16x2

Solving for variable 'x'.

Reorder the terms:
2.56 + -16x + -16x2 = 16x + -16x + 16x2 + -16x2

Combine like terms: 16x + -16x = 0
2.56 + -16x + -16x2 = 0 + 16x2 + -16x2
2.56 + -16x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
2.56 + -16x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.16 + x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.16 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.16 + 0.25

Combine like terms: 0.16 + 0.25 = 0.41
1.25 + x2 = 0.41

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.41

Calculate the square root of the right side: 0.640312424

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.640312424 and -0.640312424.

Subproblem 1
x + 0.5 = 0.640312424

Simplifying
x + 0.5 = 0.640312424

Reorder the terms:
0.5 + x = 0.640312424

Solving
0.5 + x = 0.640312424

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.640312424 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.640312424 + -0.5
x = 0.640312424 + -0.5

Combine like terms: 0.640312424 + -0.5 = 0.140312424
x = 0.140312424

Simplifying
x = 0.140312424

Subproblem 2
x + 0.5 = -0.640312424

Simplifying
x + 0.5 = -0.640312424

Reorder the terms:
0.5 + x = -0.640312424

Solving
0.5 + x = -0.640312424

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.640312424 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.640312424 + -0.5
x = -0.640312424 + -0.5

Combine like terms: -0.640312424 + -0.5 = -1.140312424
x = -1.140312424

Simplifying
x = -1.140312424

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.140312424, -1.140312424}