9x+3x(x-1900)=190000

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Solution for 9x+3x(x-1900)=190000 equation: 


Simplifying
9x + 3x(x + -1900) = 190000

Reorder the terms:
9x + 3x(-1900 + x) = 190000
9x + (-1900 * 3x + x * 3x) = 190000
9x + (-5700x + 3x2) = 190000

Combine like terms: 9x + -5700x = -5691x
-5691x + 3x2 = 190000

Solving
-5691x + 3x2 = 190000

Solving for variable 'x'.

Reorder the terms:
-190000 + -5691x + 3x2 = 190000 + -190000

Combine like terms: 190000 + -190000 = 0
-190000 + -5691x + 3x2 = 0

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

Divide each side by '3'.
-63333.33333 + -1897x + x2 = 0

Move the constant term to the right:

Add '63333.33333' to each side of the equation.
-63333.33333 + -1897x + 63333.33333 + x2 = 0 + 63333.33333

Reorder the terms:
-63333.33333 + 63333.33333 + -1897x + x2 = 0 + 63333.33333

Combine like terms: -63333.33333 + 63333.33333 = 0.00000
0.00000 + -1897x + x2 = 0 + 63333.33333
-1897x + x2 = 0 + 63333.33333

Combine like terms: 0 + 63333.33333 = 63333.33333
-1897x + x2 = 63333.33333

The x term is -1897x.  Take half its coefficient (-948.5).
Square it (899652.25) and add it to both sides.

Add '899652.25' to each side of the equation.
-1897x + 899652.25 + x2 = 63333.33333 + 899652.25

Reorder the terms:
899652.25 + -1897x + x2 = 63333.33333 + 899652.25

Combine like terms: 63333.33333 + 899652.25 = 962985.58333
899652.25 + -1897x + x2 = 962985.58333

Factor a perfect square on the left side:
(x + -948.5)(x + -948.5) = 962985.58333

Calculate the square root of the right side: 981.318288493

Break this problem into two subproblems by setting 
(x + -948.5) equal to 981.318288493 and -981.318288493.


Subproblem 1
x + -948.5 = 981.318288493

Simplifying
x + -948.5 = 981.318288493

Reorder the terms:
-948.5 + x = 981.318288493

Solving
-948.5 + x = 981.318288493

Solving for variable 'x'.

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

Add '948.5' to each side of the equation.
-948.5 + 948.5 + x = 981.318288493 + 948.5

Combine like terms: -948.5 + 948.5 = 0.0
0.0 + x = 981.318288493 + 948.5
x = 981.318288493 + 948.5

Combine like terms: 981.318288493 + 948.5 = 1929.818288493
x = 1929.818288493

Simplifying
x = 1929.818288493


Subproblem 2
x + -948.5 = -981.318288493

Simplifying
x + -948.5 = -981.318288493

Reorder the terms:
-948.5 + x = -981.318288493

Solving
-948.5 + x = -981.318288493

Solving for variable 'x'.

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

Add '948.5' to each side of the equation.
-948.5 + 948.5 + x = -981.318288493 + 948.5

Combine like terms: -948.5 + 948.5 = 0.0
0.0 + x = -981.318288493 + 948.5
x = -981.318288493 + 948.5

Combine like terms: -981.318288493 + 948.5 = -32.818288493
x = -32.818288493

Simplifying
x = -32.818288493


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1929.818288493, -32.818288493}

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