25.6x^2-16.1x-1.1=0

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Solution for 25.6x^2-16.1x-1.1=0 equation: 


Simplifying
25.6x2 + -16.1x + -1.1 = 0

Reorder the terms:
-1.1 + -16.1x + 25.6x2 = 0

Solving
-1.1 + -16.1x + 25.6x2 = 0

Solving for variable 'x'.

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

Divide each side by '25.6'.
-0.04296875 + -0.62890625x + x2 = 0

Move the constant term to the right:

Add '0.04296875' to each side of the equation.
-0.04296875 + -0.62890625x + 0.04296875 + x2 = 0 + 0.04296875

Reorder the terms:
-0.04296875 + 0.04296875 + -0.62890625x + x2 = 0 + 0.04296875

Combine like terms: -0.04296875 + 0.04296875 = 0.00000000
0.00000000 + -0.62890625x + x2 = 0 + 0.04296875
-0.62890625x + x2 = 0 + 0.04296875

Combine like terms: 0 + 0.04296875 = 0.04296875
-0.62890625x + x2 = 0.04296875

The x term is -0.62890625x.  Take half its coefficient (-0.314453125).
Square it (0.09888076782) and add it to both sides.

Add '0.09888076782' to each side of the equation.
-0.62890625x + 0.09888076782 + x2 = 0.04296875 + 0.09888076782

Reorder the terms:
0.09888076782 + -0.62890625x + x2 = 0.04296875 + 0.09888076782

Combine like terms: 0.04296875 + 0.09888076782 = 0.14184951782
0.09888076782 + -0.62890625x + x2 = 0.14184951782

Factor a perfect square on the left side:
(x + -0.314453125)(x + -0.314453125) = 0.14184951782

Calculate the square root of the right side: 0.376629152

Break this problem into two subproblems by setting 
(x + -0.314453125) equal to 0.376629152 and -0.376629152.


Subproblem 1
x + -0.314453125 = 0.376629152

Simplifying
x + -0.314453125 = 0.376629152

Reorder the terms:
-0.314453125 + x = 0.376629152

Solving
-0.314453125 + x = 0.376629152

Solving for variable 'x'.

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

Add '0.314453125' to each side of the equation.
-0.314453125 + 0.314453125 + x = 0.376629152 + 0.314453125

Combine like terms: -0.314453125 + 0.314453125 = 0.000000000
0.000000000 + x = 0.376629152 + 0.314453125
x = 0.376629152 + 0.314453125

Combine like terms: 0.376629152 + 0.314453125 = 0.691082277
x = 0.691082277

Simplifying
x = 0.691082277


Subproblem 2
x + -0.314453125 = -0.376629152

Simplifying
x + -0.314453125 = -0.376629152

Reorder the terms:
-0.314453125 + x = -0.376629152

Solving
-0.314453125 + x = -0.376629152

Solving for variable 'x'.

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

Add '0.314453125' to each side of the equation.
-0.314453125 + 0.314453125 + x = -0.376629152 + 0.314453125

Combine like terms: -0.314453125 + 0.314453125 = 0.000000000
0.000000000 + x = -0.376629152 + 0.314453125
x = -0.376629152 + 0.314453125

Combine like terms: -0.376629152 + 0.314453125 = -0.062176027
x = -0.062176027

Simplifying
x = -0.062176027


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.691082277, -0.062176027}

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