84000=50x+(0.2x^2)

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Solution for 84000=50x+(0.2x^2) equation: 


Simplifying
84000 = 50x + (0.2x2)

Solving
84000 = 50x + (0.2x2)

Solving for variable 'x'.

Reorder the terms:
84000 + -50x + (-0.2x2) = 50x + -50x + (0.2x2) + (-0.2x2)

Combine like terms: 50x + -50x = 0
84000 + -50x + (-0.2x2) = 0 + (0.2x2) + (-0.2x2)
84000 + -50x + (-0.2x2) = (0.2x2) + (-0.2x2)

Combine like terms: (0.2x2) + (-0.2x2) = 0.0
84000 + -50x + (-0.2x2) = 0.0

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
-420000 + 250x + x2 = 0

Move the constant term to the right:

Add '420000' to each side of the equation.
-420000 + 250x + 420000 + x2 = 0 + 420000

Reorder the terms:
-420000 + 420000 + 250x + x2 = 0 + 420000

Combine like terms: -420000 + 420000 = 0
0 + 250x + x2 = 0 + 420000
250x + x2 = 0 + 420000

Combine like terms: 0 + 420000 = 420000
250x + x2 = 420000

The x term is 250x.  Take half its coefficient (125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
250x + 15625 + x2 = 420000 + 15625

Reorder the terms:
15625 + 250x + x2 = 420000 + 15625

Combine like terms: 420000 + 15625 = 435625
15625 + 250x + x2 = 435625

Factor a perfect square on the left side:
((x) + 125)((x) + 125) = 435625

Calculate the square root of the right side: 660.018939122

Break this problem into two subproblems by setting 
((x) + 125) equal to 660.018939122 and -660.018939122.


Subproblem 1
(x) + 125 = 660.018939122

Simplifying
(x) + 125 = 660.018939122
x + 125 = 660.018939122

Reorder the terms:
125 + x = 660.018939122

Solving
125 + x = 660.018939122

Solving for variable 'x'.

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

Add '-125' to each side of the equation.
125 + -125 + x = 660.018939122 + -125

Combine like terms: 125 + -125 = 0
0 + x = 660.018939122 + -125
x = 660.018939122 + -125

Combine like terms: 660.018939122 + -125 = 535.018939122
x = 535.018939122

Simplifying
x = 535.018939122


Subproblem 2
(x) + 125 = -660.018939122

Simplifying
(x) + 125 = -660.018939122
x + 125 = -660.018939122

Reorder the terms:
125 + x = -660.018939122

Solving
125 + x = -660.018939122

Solving for variable 'x'.

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

Add '-125' to each side of the equation.
125 + -125 + x = -660.018939122 + -125

Combine like terms: 125 + -125 = 0
0 + x = -660.018939122 + -125
x = -660.018939122 + -125

Combine like terms: -660.018939122 + -125 = -785.018939122
x = -785.018939122

Simplifying
x = -785.018939122


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {535.018939122, -785.018939122}

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