16x^2-16x+2.56=0

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Solution for 16x^2-16x+2.56=0 equation: 


Simplifying
16x2 + -16x + 2.56 = 0

Reorder the terms:
2.56 + -16x + 16x2 = 0

Solving
2.56 + -16x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
0.16 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + -1x + -0.16 + x2 = 0 + -0.16

Reorder the terms:
0.16 + -0.16 + -1x + x2 = 0 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + -1x + x2 = 0 + -0.16
-1x + x2 = 0 + -0.16

Combine like terms: 0 + -0.16 = -0.16
-1x + x2 = -0.16

The x term is -1x.  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.
-1x + 0.25 + x2 = -0.16 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.16 + 0.25

Combine like terms: -0.16 + 0.25 = 0.09
0.25 + -1x + x2 = 0.09

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.09

Calculate the square root of the right side: 0.3

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.3 and -0.3.


Subproblem 1
x + -0.5 = 0.3

Simplifying
x + -0.5 = 0.3

Reorder the terms:
-0.5 + x = 0.3

Solving
-0.5 + x = 0.3

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 = 0.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.3 + 0.5
x = 0.3 + 0.5

Combine like terms: 0.3 + 0.5 = 0.8
x = 0.8

Simplifying
x = 0.8


Subproblem 2
x + -0.5 = -0.3

Simplifying
x + -0.5 = -0.3

Reorder the terms:
-0.5 + x = -0.3

Solving
-0.5 + x = -0.3

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 = -0.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.3 + 0.5
x = -0.3 + 0.5

Combine like terms: -0.3 + 0.5 = 0.2
x = 0.2

Simplifying
x = 0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8, 0.2}

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