3.2x^2-x-1=0

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Solution for 3.2x^2-x-1=0 equation: 


Simplifying
3.2x2 + -1x + -1 = 0

Reorder the terms:
-1 + -1x + 3.2x2 = 0

Solving
-1 + -1x + 3.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.2'.
-0.3125 + -0.3125x + x2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -0.3125x + 0.3125 + x2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -0.3125x + x2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -0.3125x + x2 = 0 + 0.3125
-0.3125x + x2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-0.3125x + x2 = 0.3125

The x term is -0.3125x.  Take half its coefficient (-0.15625).
Square it (0.0244140625) and add it to both sides.

Add '0.0244140625' to each side of the equation.
-0.3125x + 0.0244140625 + x2 = 0.3125 + 0.0244140625

Reorder the terms:
0.0244140625 + -0.3125x + x2 = 0.3125 + 0.0244140625

Combine like terms: 0.3125 + 0.0244140625 = 0.3369140625
0.0244140625 + -0.3125x + x2 = 0.3369140625

Factor a perfect square on the left side:
(x + -0.15625)(x + -0.15625) = 0.3369140625

Calculate the square root of the right side: 0.580442988

Break this problem into two subproblems by setting 
(x + -0.15625) equal to 0.580442988 and -0.580442988.


Subproblem 1
x + -0.15625 = 0.580442988

Simplifying
x + -0.15625 = 0.580442988

Reorder the terms:
-0.15625 + x = 0.580442988

Solving
-0.15625 + x = 0.580442988

Solving for variable 'x'.

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

Add '0.15625' to each side of the equation.
-0.15625 + 0.15625 + x = 0.580442988 + 0.15625

Combine like terms: -0.15625 + 0.15625 = 0.00000
0.00000 + x = 0.580442988 + 0.15625
x = 0.580442988 + 0.15625

Combine like terms: 0.580442988 + 0.15625 = 0.736692988
x = 0.736692988

Simplifying
x = 0.736692988


Subproblem 2
x + -0.15625 = -0.580442988

Simplifying
x + -0.15625 = -0.580442988

Reorder the terms:
-0.15625 + x = -0.580442988

Solving
-0.15625 + x = -0.580442988

Solving for variable 'x'.

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

Add '0.15625' to each side of the equation.
-0.15625 + 0.15625 + x = -0.580442988 + 0.15625

Combine like terms: -0.15625 + 0.15625 = 0.00000
0.00000 + x = -0.580442988 + 0.15625
x = -0.580442988 + 0.15625

Combine like terms: -0.580442988 + 0.15625 = -0.424192988
x = -0.424192988

Simplifying
x = -0.424192988


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.736692988, -0.424192988}

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