x(1+0.075x)=60000

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Solution for x(1+0.075x)=60000 equation: 


Simplifying
x(1 + 0.075x) = 60000
(1 * x + 0.075x * x) = 60000
(1x + 0.075x2) = 60000

Solving
1x + 0.075x2 = 60000

Solving for variable 'x'.

Reorder the terms:
-60000 + 1x + 0.075x2 = 60000 + -60000

Combine like terms: 60000 + -60000 = 0
-60000 + 1x + 0.075x2 = 0

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

Divide each side by '0.075'.
-800000 + 13.33333333x + x2 = 0

Move the constant term to the right:

Add '800000' to each side of the equation.
-800000 + 13.33333333x + 800000 + x2 = 0 + 800000

Reorder the terms:
-800000 + 800000 + 13.33333333x + x2 = 0 + 800000

Combine like terms: -800000 + 800000 = 0
0 + 13.33333333x + x2 = 0 + 800000
13.33333333x + x2 = 0 + 800000

Combine like terms: 0 + 800000 = 800000
13.33333333x + x2 = 800000

The x term is 13.33333333x.  Take half its coefficient (6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
13.33333333x + 44.44444442 + x2 = 800000 + 44.44444442

Reorder the terms:
44.44444442 + 13.33333333x + x2 = 800000 + 44.44444442

Combine like terms: 800000 + 44.44444442 = 800044.44444442
44.44444442 + 13.33333333x + x2 = 800044.44444442

Factor a perfect square on the left side:
(x + 6.666666665)(x + 6.666666665) = 800044.44444442

Calculate the square root of the right side: 894.452035855

Break this problem into two subproblems by setting 
(x + 6.666666665) equal to 894.452035855 and -894.452035855.


Subproblem 1
x + 6.666666665 = 894.452035855

Simplifying
x + 6.666666665 = 894.452035855

Reorder the terms:
6.666666665 + x = 894.452035855

Solving
6.666666665 + x = 894.452035855

Solving for variable 'x'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + x = 894.452035855 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + x = 894.452035855 + -6.666666665
x = 894.452035855 + -6.666666665

Combine like terms: 894.452035855 + -6.666666665 = 887.78536919
x = 887.78536919

Simplifying
x = 887.78536919


Subproblem 2
x + 6.666666665 = -894.452035855

Simplifying
x + 6.666666665 = -894.452035855

Reorder the terms:
6.666666665 + x = -894.452035855

Solving
6.666666665 + x = -894.452035855

Solving for variable 'x'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + x = -894.452035855 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + x = -894.452035855 + -6.666666665
x = -894.452035855 + -6.666666665

Combine like terms: -894.452035855 + -6.666666665 = -901.11870252
x = -901.11870252

Simplifying
x = -901.11870252


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {887.78536919, -901.11870252}

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