800x^2-17x-8.5=0

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Solution for 800x^2-17x-8.5=0 equation: 


Simplifying
800x2 + -17x + -8.5 = 0

Reorder the terms:
-8.5 + -17x + 800x2 = 0

Solving
-8.5 + -17x + 800x2 = 0

Solving for variable 'x'.

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

Divide each side by '800'.
-0.010625 + -0.02125x + x2 = 0

Move the constant term to the right:

Add '0.010625' to each side of the equation.
-0.010625 + -0.02125x + 0.010625 + x2 = 0 + 0.010625

Reorder the terms:
-0.010625 + 0.010625 + -0.02125x + x2 = 0 + 0.010625

Combine like terms: -0.010625 + 0.010625 = 0.000000
0.000000 + -0.02125x + x2 = 0 + 0.010625
-0.02125x + x2 = 0 + 0.010625

Combine like terms: 0 + 0.010625 = 0.010625
-0.02125x + x2 = 0.010625

The x term is -0.02125x.  Take half its coefficient (-0.010625).
Square it (0.000112890625) and add it to both sides.

Add '0.000112890625' to each side of the equation.
-0.02125x + 0.000112890625 + x2 = 0.010625 + 0.000112890625

Reorder the terms:
0.000112890625 + -0.02125x + x2 = 0.010625 + 0.000112890625

Combine like terms: 0.010625 + 0.000112890625 = 0.010737890625
0.000112890625 + -0.02125x + x2 = 0.010737890625

Factor a perfect square on the left side:
(x + -0.010625)(x + -0.010625) = 0.010737890625

Calculate the square root of the right side: 0.103623794

Break this problem into two subproblems by setting 
(x + -0.010625) equal to 0.103623794 and -0.103623794.


Subproblem 1
x + -0.010625 = 0.103623794

Simplifying
x + -0.010625 = 0.103623794

Reorder the terms:
-0.010625 + x = 0.103623794

Solving
-0.010625 + x = 0.103623794

Solving for variable 'x'.

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

Add '0.010625' to each side of the equation.
-0.010625 + 0.010625 + x = 0.103623794 + 0.010625

Combine like terms: -0.010625 + 0.010625 = 0.000000
0.000000 + x = 0.103623794 + 0.010625
x = 0.103623794 + 0.010625

Combine like terms: 0.103623794 + 0.010625 = 0.114248794
x = 0.114248794

Simplifying
x = 0.114248794


Subproblem 2
x + -0.010625 = -0.103623794

Simplifying
x + -0.010625 = -0.103623794

Reorder the terms:
-0.010625 + x = -0.103623794

Solving
-0.010625 + x = -0.103623794

Solving for variable 'x'.

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

Add '0.010625' to each side of the equation.
-0.010625 + 0.010625 + x = -0.103623794 + 0.010625

Combine like terms: -0.010625 + 0.010625 = 0.000000
0.000000 + x = -0.103623794 + 0.010625
x = -0.103623794 + 0.010625

Combine like terms: -0.103623794 + 0.010625 = -0.092998794
x = -0.092998794

Simplifying
x = -0.092998794


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.114248794, -0.092998794}

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