8.58=0.001(0.732x^2+15.417x+609.738)

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Solution for 8.58=0.001(0.732x^2+15.417x+609.738) equation: 


Simplifying
8.58 = 0.001(0.732x2 + 15.417x + 609.738)

Reorder the terms:
8.58 = 0.001(609.738 + 15.417x + 0.732x2)
8.58 = (609.738 * 0.001 + 15.417x * 0.001 + 0.732x2 * 0.001)
8.58 = (0.609738 + 0.015417x + 0.000732x2)

Solving
8.58 = 0.609738 + 0.015417x + 0.000732x2

Solving for variable 'x'.

Combine like terms: 8.58 + -0.609738 = 7.970262
7.970262 + -0.015417x + -0.000732x2 = 0.609738 + 0.015417x + 0.000732x2 + -0.609738 + -0.015417x + -0.000732x2

Reorder the terms:
7.970262 + -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
7.970262 + -0.015417x + -0.000732x2 = 0.000000 + 0.015417x + -0.015417x + 0.000732x2 + -0.000732x2
7.970262 + -0.015417x + -0.000732x2 = 0.015417x + -0.015417x + 0.000732x2 + -0.000732x2

Combine like terms: 0.015417x + -0.015417x = 0.000000
7.970262 + -0.015417x + -0.000732x2 = 0.000000 + 0.000732x2 + -0.000732x2
7.970262 + -0.015417x + -0.000732x2 = 0.000732x2 + -0.000732x2

Combine like terms: 0.000732x2 + -0.000732x2 = 0.000000
7.970262 + -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'.
-10888.33607 + 21.06147541x + x2 = 0

Move the constant term to the right:

Add '10888.33607' to each side of the equation.
-10888.33607 + 21.06147541x + 10888.33607 + x2 = 0 + 10888.33607

Reorder the terms:
-10888.33607 + 10888.33607 + 21.06147541x + x2 = 0 + 10888.33607

Combine like terms: -10888.33607 + 10888.33607 = 0.00000
0.00000 + 21.06147541x + x2 = 0 + 10888.33607
21.06147541x + x2 = 0 + 10888.33607

Combine like terms: 0 + 10888.33607 = 10888.33607
21.06147541x + x2 = 10888.33607

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 = 10888.33607 + 110.8964367

Reorder the terms:
110.8964367 + 21.06147541x + x2 = 10888.33607 + 110.8964367

Combine like terms: 10888.33607 + 110.8964367 = 10999.2325067
110.8964367 + 21.06147541x + x2 = 10999.2325067

Factor a perfect square on the left side:
(x + 10.53073771)(x + 10.53073771) = 10999.2325067

Calculate the square root of the right side: 104.877225872

Break this problem into two subproblems by setting 
(x + 10.53073771) equal to 104.877225872 and -104.877225872.


Subproblem 1
x + 10.53073771 = 104.877225872

Simplifying
x + 10.53073771 = 104.877225872

Reorder the terms:
10.53073771 + x = 104.877225872

Solving
10.53073771 + x = 104.877225872

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 = 104.877225872 + -10.53073771

Combine like terms: 10.53073771 + -10.53073771 = 0.00000000
0.00000000 + x = 104.877225872 + -10.53073771
x = 104.877225872 + -10.53073771

Combine like terms: 104.877225872 + -10.53073771 = 94.346488162
x = 94.346488162

Simplifying
x = 94.346488162


Subproblem 2
x + 10.53073771 = -104.877225872

Simplifying
x + 10.53073771 = -104.877225872

Reorder the terms:
10.53073771 + x = -104.877225872

Solving
10.53073771 + x = -104.877225872

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 = -104.877225872 + -10.53073771

Combine like terms: 10.53073771 + -10.53073771 = 0.00000000
0.00000000 + x = -104.877225872 + -10.53073771
x = -104.877225872 + -10.53073771

Combine like terms: -104.877225872 + -10.53073771 = -115.407963582
x = -115.407963582

Simplifying
x = -115.407963582


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {94.346488162, -115.407963582}

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