(32x^2-3x-6.5)=0

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Solution for (32x^2-3x-6.5)=0 equation: 


Simplifying
(32x2 + -3x + -6.5) = 0

Reorder the terms:
(-6.5 + -3x + 32x2) = 0

Remove parenthesis around (-6.5 + -3x + 32x2)
-6.5 + -3x + 32x2 = 0

Solving
-6.5 + -3x + 32x2 = 0

Solving for variable 'x'.

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

Divide each side by '32'.
-0.203125 + -0.09375x + x2 = 0

Move the constant term to the right:

Add '0.203125' to each side of the equation.
-0.203125 + -0.09375x + 0.203125 + x2 = 0 + 0.203125

Reorder the terms:
-0.203125 + 0.203125 + -0.09375x + x2 = 0 + 0.203125

Combine like terms: -0.203125 + 0.203125 = 0.000000
0.000000 + -0.09375x + x2 = 0 + 0.203125
-0.09375x + x2 = 0 + 0.203125

Combine like terms: 0 + 0.203125 = 0.203125
-0.09375x + x2 = 0.203125

The x term is -0.09375x.  Take half its coefficient (-0.046875).
Square it (0.002197265625) and add it to both sides.

Add '0.002197265625' to each side of the equation.
-0.09375x + 0.002197265625 + x2 = 0.203125 + 0.002197265625

Reorder the terms:
0.002197265625 + -0.09375x + x2 = 0.203125 + 0.002197265625

Combine like terms: 0.203125 + 0.002197265625 = 0.205322265625
0.002197265625 + -0.09375x + x2 = 0.205322265625

Factor a perfect square on the left side:
(x + -0.046875)(x + -0.046875) = 0.205322265625

Calculate the square root of the right side: 0.453125

Break this problem into two subproblems by setting 
(x + -0.046875) equal to 0.453125 and -0.453125.


Subproblem 1
x + -0.046875 = 0.453125

Simplifying
x + -0.046875 = 0.453125

Reorder the terms:
-0.046875 + x = 0.453125

Solving
-0.046875 + x = 0.453125

Solving for variable 'x'.

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

Add '0.046875' to each side of the equation.
-0.046875 + 0.046875 + x = 0.453125 + 0.046875

Combine like terms: -0.046875 + 0.046875 = 0.000000
0.000000 + x = 0.453125 + 0.046875
x = 0.453125 + 0.046875

Combine like terms: 0.453125 + 0.046875 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + -0.046875 = -0.453125

Simplifying
x + -0.046875 = -0.453125

Reorder the terms:
-0.046875 + x = -0.453125

Solving
-0.046875 + x = -0.453125

Solving for variable 'x'.

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

Add '0.046875' to each side of the equation.
-0.046875 + 0.046875 + x = -0.453125 + 0.046875

Combine like terms: -0.046875 + 0.046875 = 0.000000
0.000000 + x = -0.453125 + 0.046875
x = -0.453125 + 0.046875

Combine like terms: -0.453125 + 0.046875 = -0.40625
x = -0.40625

Simplifying
x = -0.40625


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -0.40625}

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