x^2-1.6x-2.56=0

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Solution for x^2-1.6x-2.56=0 equation: 


Simplifying
x2 + -1.6x + -2.56 = 0

Reorder the terms:
-2.56 + -1.6x + x2 = 0

Solving
-2.56 + -1.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.56' to each side of the equation.
-2.56 + -1.6x + 2.56 + x2 = 0 + 2.56

Reorder the terms:
-2.56 + 2.56 + -1.6x + x2 = 0 + 2.56

Combine like terms: -2.56 + 2.56 = 0.00
0.00 + -1.6x + x2 = 0 + 2.56
-1.6x + x2 = 0 + 2.56

Combine like terms: 0 + 2.56 = 2.56
-1.6x + x2 = 2.56

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 2.56 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 2.56 + 0.64

Combine like terms: 2.56 + 0.64 = 3.2
0.64 + -1.6x + x2 = 3.2

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 3.2

Calculate the square root of the right side: 1.788854382

Break this problem into two subproblems by setting 
(x + -0.8) equal to 1.788854382 and -1.788854382.


Subproblem 1
x + -0.8 = 1.788854382

Simplifying
x + -0.8 = 1.788854382

Reorder the terms:
-0.8 + x = 1.788854382

Solving
-0.8 + x = 1.788854382

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = 1.788854382 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = 1.788854382 + 0.8
x = 1.788854382 + 0.8

Combine like terms: 1.788854382 + 0.8 = 2.588854382
x = 2.588854382

Simplifying
x = 2.588854382


Subproblem 2
x + -0.8 = -1.788854382

Simplifying
x + -0.8 = -1.788854382

Reorder the terms:
-0.8 + x = -1.788854382

Solving
-0.8 + x = -1.788854382

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = -1.788854382 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = -1.788854382 + 0.8
x = -1.788854382 + 0.8

Combine like terms: -1.788854382 + 0.8 = -0.988854382
x = -0.988854382

Simplifying
x = -0.988854382


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.588854382, -0.988854382}

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