.75x^2+35000x-200=0

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Solution for .75x^2+35000x-200=0 equation: 


Simplifying
0.75x2 + 35000x + -200 = 0

Reorder the terms:
-200 + 35000x + 0.75x2 = 0

Solving
-200 + 35000x + 0.75x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.75'.
-266.6666667 + 46666.66667x + x2 = 0

Move the constant term to the right:

Add '266.6666667' to each side of the equation.
-266.6666667 + 46666.66667x + 266.6666667 + x2 = 0 + 266.6666667

Reorder the terms:
-266.6666667 + 266.6666667 + 46666.66667x + x2 = 0 + 266.6666667

Combine like terms: -266.6666667 + 266.6666667 = 0.0000000
0.0000000 + 46666.66667x + x2 = 0 + 266.6666667
46666.66667x + x2 = 0 + 266.6666667

Combine like terms: 0 + 266.6666667 = 266.6666667
46666.66667x + x2 = 266.6666667

The x term is 46666.66667x.  Take half its coefficient (23333.33334).
Square it (544444444.8) and add it to both sides.

Add '544444444.8' to each side of the equation.
46666.66667x + 544444444.8 + x2 = 266.6666667 + 544444444.8

Reorder the terms:
544444444.8 + 46666.66667x + x2 = 266.6666667 + 544444444.8

Combine like terms: 266.6666667 + 544444444.8 = 544444711.4666667
544444444.8 + 46666.66667x + x2 = 544444711.4666667

Factor a perfect square on the left side:
(x + 23333.33334)(x + 23333.33334) = 544444711.4666667

Calculate the square root of the right side: 23333.339055237

Break this problem into two subproblems by setting 
(x + 23333.33334) equal to 23333.339055237 and -23333.339055237.


Subproblem 1
x + 23333.33334 = 23333.339055237

Simplifying
x + 23333.33334 = 23333.339055237

Reorder the terms:
23333.33334 + x = 23333.339055237

Solving
23333.33334 + x = 23333.339055237

Solving for variable 'x'.

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

Add '-23333.33334' to each side of the equation.
23333.33334 + -23333.33334 + x = 23333.339055237 + -23333.33334

Combine like terms: 23333.33334 + -23333.33334 = 0.00000
0.00000 + x = 23333.339055237 + -23333.33334
x = 23333.339055237 + -23333.33334

Combine like terms: 23333.339055237 + -23333.33334 = 0.005715237
x = 0.005715237

Simplifying
x = 0.005715237


Subproblem 2
x + 23333.33334 = -23333.339055237

Simplifying
x + 23333.33334 = -23333.339055237

Reorder the terms:
23333.33334 + x = -23333.339055237

Solving
23333.33334 + x = -23333.339055237

Solving for variable 'x'.

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

Add '-23333.33334' to each side of the equation.
23333.33334 + -23333.33334 + x = -23333.339055237 + -23333.33334

Combine like terms: 23333.33334 + -23333.33334 = 0.00000
0.00000 + x = -23333.339055237 + -23333.33334
x = -23333.339055237 + -23333.33334

Combine like terms: -23333.339055237 + -23333.33334 = -46666.672395237
x = -46666.672395237

Simplifying
x = -46666.672395237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.005715237, -46666.672395237}

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