.0001x^2+.05x-2.3=0

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Solution for .0001x^2+.05x-2.3=0 equation: 


Simplifying
0.0001x2 + 0.05x + -2.3 = 0

Reorder the terms:
-2.3 + 0.05x + 0.0001x2 = 0

Solving
-2.3 + 0.05x + 0.0001x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0001 the coefficient of the squared term: 

Divide each side by '0.0001'.
-23000 + 500x + x2 = 0

Move the constant term to the right:

Add '23000' to each side of the equation.
-23000 + 500x + 23000 + x2 = 0 + 23000

Reorder the terms:
-23000 + 23000 + 500x + x2 = 0 + 23000

Combine like terms: -23000 + 23000 = 0
0 + 500x + x2 = 0 + 23000
500x + x2 = 0 + 23000

Combine like terms: 0 + 23000 = 23000
500x + x2 = 23000

The x term is 500x.  Take half its coefficient (250).
Square it (62500) and add it to both sides.

Add '62500' to each side of the equation.
500x + 62500 + x2 = 23000 + 62500

Reorder the terms:
62500 + 500x + x2 = 23000 + 62500

Combine like terms: 23000 + 62500 = 85500
62500 + 500x + x2 = 85500

Factor a perfect square on the left side:
(x + 250)(x + 250) = 85500

Calculate the square root of the right side: 292.403830344

Break this problem into two subproblems by setting 
(x + 250) equal to 292.403830344 and -292.403830344.


Subproblem 1
x + 250 = 292.403830344

Simplifying
x + 250 = 292.403830344

Reorder the terms:
250 + x = 292.403830344

Solving
250 + x = 292.403830344

Solving for variable 'x'.

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

Add '-250' to each side of the equation.
250 + -250 + x = 292.403830344 + -250

Combine like terms: 250 + -250 = 0
0 + x = 292.403830344 + -250
x = 292.403830344 + -250

Combine like terms: 292.403830344 + -250 = 42.403830344
x = 42.403830344

Simplifying
x = 42.403830344


Subproblem 2
x + 250 = -292.403830344

Simplifying
x + 250 = -292.403830344

Reorder the terms:
250 + x = -292.403830344

Solving
250 + x = -292.403830344

Solving for variable 'x'.

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

Add '-250' to each side of the equation.
250 + -250 + x = -292.403830344 + -250

Combine like terms: 250 + -250 = 0
0 + x = -292.403830344 + -250
x = -292.403830344 + -250

Combine like terms: -292.403830344 + -250 = -542.403830344
x = -542.403830344

Simplifying
x = -542.403830344


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.403830344, -542.403830344}

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