8.59=0.001(0.732x^2+15.417x+609.738)

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Solution for 8.59=0.001(0.732x^2+15.417x+609.738) equation: 


Simplifying
8.59 = 0.001(0.732x2 + 15.417x + 609.738)

Reorder the terms:
8.59 = 0.001(609.738 + 15.417x + 0.732x2)
8.59 = (609.738 * 0.001 + 15.417x * 0.001 + 0.732x2 * 0.001)
8.59 = (0.609738 + 0.015417x + 0.000732x2)

Solving
8.59 = 0.609738 + 0.015417x + 0.000732x2

Solving for variable 'x'.

Combine like terms: 8.59 + -0.609738 = 7.980262
7.980262 + -0.015417x + -0.000732x2 = 0.609738 + 0.015417x + 0.000732x2 + -0.609738 + -0.015417x + -0.000732x2

Reorder the terms:
7.980262 + -0.015417x + -0.000732x2 = 0.609738 + -0.609738 + 0.015417x + -0.015417x + 0.000732x2 + -0.000732x2

Combine like terms: 0.609738 + -0.609738 = 0.000000
7.980262 + -0.015417x + -0.000732x2 = 0.000000 + 0.015417x + -0.015417x + 0.000732x2 + -0.000732x2
7.980262 + -0.015417x + -0.000732x2 = 0.015417x + -0.015417x + 0.000732x2 + -0.000732x2

Combine like terms: 0.015417x + -0.015417x = 0.000000
7.980262 + -0.015417x + -0.000732x2 = 0.000000 + 0.000732x2 + -0.000732x2
7.980262 + -0.015417x + -0.000732x2 = 0.000732x2 + -0.000732x2

Combine like terms: 0.000732x2 + -0.000732x2 = 0.000000
7.980262 + -0.015417x + -0.000732x2 = 0.000000

Begin completing the square.  Divide all terms by
-0.000732 the coefficient of the squared term: 

Divide each side by '-0.000732'.
-10901.99727 + 21.06147541x + x2 = 0

Move the constant term to the right:

Add '10901.99727' to each side of the equation.
-10901.99727 + 21.06147541x + 10901.99727 + x2 = 0 + 10901.99727

Reorder the terms:
-10901.99727 + 10901.99727 + 21.06147541x + x2 = 0 + 10901.99727

Combine like terms: -10901.99727 + 10901.99727 = 0.00000
0.00000 + 21.06147541x + x2 = 0 + 10901.99727
21.06147541x + x2 = 0 + 10901.99727

Combine like terms: 0 + 10901.99727 = 10901.99727
21.06147541x + x2 = 10901.99727

The x term is 21.06147541x.  Take half its coefficient (10.53073771).
Square it (110.8964367) and add it to both sides.

Add '110.8964367' to each side of the equation.
21.06147541x + 110.8964367 + x2 = 10901.99727 + 110.8964367

Reorder the terms:
110.8964367 + 21.06147541x + x2 = 10901.99727 + 110.8964367

Combine like terms: 10901.99727 + 110.8964367 = 11012.8937067
110.8964367 + 21.06147541x + x2 = 11012.8937067

Factor a perfect square on the left side:
(x + 10.53073771)(x + 10.53073771) = 11012.8937067

Calculate the square root of the right side: 104.94233515

Break this problem into two subproblems by setting 
(x + 10.53073771) equal to 104.94233515 and -104.94233515.


Subproblem 1
x + 10.53073771 = 104.94233515

Simplifying
x + 10.53073771 = 104.94233515

Reorder the terms:
10.53073771 + x = 104.94233515

Solving
10.53073771 + x = 104.94233515

Solving for variable 'x'.

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

Add '-10.53073771' to each side of the equation.
10.53073771 + -10.53073771 + x = 104.94233515 + -10.53073771

Combine like terms: 10.53073771 + -10.53073771 = 0.00000000
0.00000000 + x = 104.94233515 + -10.53073771
x = 104.94233515 + -10.53073771

Combine like terms: 104.94233515 + -10.53073771 = 94.41159744
x = 94.41159744

Simplifying
x = 94.41159744


Subproblem 2
x + 10.53073771 = -104.94233515

Simplifying
x + 10.53073771 = -104.94233515

Reorder the terms:
10.53073771 + x = -104.94233515

Solving
10.53073771 + x = -104.94233515

Solving for variable 'x'.

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

Add '-10.53073771' to each side of the equation.
10.53073771 + -10.53073771 + x = -104.94233515 + -10.53073771

Combine like terms: 10.53073771 + -10.53073771 = 0.00000000
0.00000000 + x = -104.94233515 + -10.53073771
x = -104.94233515 + -10.53073771

Combine like terms: -104.94233515 + -10.53073771 = -115.47307286
x = -115.47307286

Simplifying
x = -115.47307286


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {94.41159744, -115.47307286}

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