8.99=0.001(0.73x^2+15.417x+607.738)

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Solution for 8.99=0.001(0.73x^2+15.417x+607.738) equation: 


Simplifying
8.99 = 0.001(0.73x2 + 15.417x + 607.738)

Reorder the terms:
8.99 = 0.001(607.738 + 15.417x + 0.73x2)
8.99 = (607.738 * 0.001 + 15.417x * 0.001 + 0.73x2 * 0.001)
8.99 = (0.607738 + 0.015417x + 0.00073x2)

Solving
8.99 = 0.607738 + 0.015417x + 0.00073x2

Solving for variable 'x'.

Combine like terms: 8.99 + -0.607738 = 8.382262
8.382262 + -0.015417x + -0.00073x2 = 0.607738 + 0.015417x + 0.00073x2 + -0.607738 + -0.015417x + -0.00073x2

Reorder the terms:
8.382262 + -0.015417x + -0.00073x2 = 0.607738 + -0.607738 + 0.015417x + -0.015417x + 0.00073x2 + -0.00073x2

Combine like terms: 0.607738 + -0.607738 = 0.000000
8.382262 + -0.015417x + -0.00073x2 = 0.000000 + 0.015417x + -0.015417x + 0.00073x2 + -0.00073x2
8.382262 + -0.015417x + -0.00073x2 = 0.015417x + -0.015417x + 0.00073x2 + -0.00073x2

Combine like terms: 0.015417x + -0.015417x = 0.000000
8.382262 + -0.015417x + -0.00073x2 = 0.000000 + 0.00073x2 + -0.00073x2
8.382262 + -0.015417x + -0.00073x2 = 0.00073x2 + -0.00073x2

Combine like terms: 0.00073x2 + -0.00073x2 = 0.00000
8.382262 + -0.015417x + -0.00073x2 = 0.00000

Begin completing the square.  Divide all terms by
-0.00073 the coefficient of the squared term: 

Divide each side by '-0.00073'.
-11482.55068 + 21.11917808x + x2 = 0

Move the constant term to the right:

Add '11482.55068' to each side of the equation.
-11482.55068 + 21.11917808x + 11482.55068 + x2 = 0 + 11482.55068

Reorder the terms:
-11482.55068 + 11482.55068 + 21.11917808x + x2 = 0 + 11482.55068

Combine like terms: -11482.55068 + 11482.55068 = 0.00000
0.00000 + 21.11917808x + x2 = 0 + 11482.55068
21.11917808x + x2 = 0 + 11482.55068

Combine like terms: 0 + 11482.55068 = 11482.55068
21.11917808x + x2 = 11482.55068

The x term is 21.11917808x.  Take half its coefficient (10.55958904).
Square it (111.5049207) and add it to both sides.

Add '111.5049207' to each side of the equation.
21.11917808x + 111.5049207 + x2 = 11482.55068 + 111.5049207

Reorder the terms:
111.5049207 + 21.11917808x + x2 = 11482.55068 + 111.5049207

Combine like terms: 11482.55068 + 111.5049207 = 11594.0556007
111.5049207 + 21.11917808x + x2 = 11594.0556007

Factor a perfect square on the left side:
(x + 10.55958904)(x + 10.55958904) = 11594.0556007

Calculate the square root of the right side: 107.675696425

Break this problem into two subproblems by setting 
(x + 10.55958904) equal to 107.675696425 and -107.675696425.


Subproblem 1
x + 10.55958904 = 107.675696425

Simplifying
x + 10.55958904 = 107.675696425

Reorder the terms:
10.55958904 + x = 107.675696425

Solving
10.55958904 + x = 107.675696425

Solving for variable 'x'.

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

Add '-10.55958904' to each side of the equation.
10.55958904 + -10.55958904 + x = 107.675696425 + -10.55958904

Combine like terms: 10.55958904 + -10.55958904 = 0.00000000
0.00000000 + x = 107.675696425 + -10.55958904
x = 107.675696425 + -10.55958904

Combine like terms: 107.675696425 + -10.55958904 = 97.116107385
x = 97.116107385

Simplifying
x = 97.116107385


Subproblem 2
x + 10.55958904 = -107.675696425

Simplifying
x + 10.55958904 = -107.675696425

Reorder the terms:
10.55958904 + x = -107.675696425

Solving
10.55958904 + x = -107.675696425

Solving for variable 'x'.

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

Add '-10.55958904' to each side of the equation.
10.55958904 + -10.55958904 + x = -107.675696425 + -10.55958904

Combine like terms: 10.55958904 + -10.55958904 = 0.00000000
0.00000000 + x = -107.675696425 + -10.55958904
x = -107.675696425 + -10.55958904

Combine like terms: -107.675696425 + -10.55958904 = -118.235285465
x = -118.235285465

Simplifying
x = -118.235285465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {97.116107385, -118.235285465}

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