0.08x-1.9+0.0001x^2=0

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Solution for 0.08x-1.9+0.0001x^2=0 equation: 


Simplifying
0.08x + -1.9 + 0.0001x2 = 0

Reorder the terms:
-1.9 + 0.08x + 0.0001x2 = 0

Solving
-1.9 + 0.08x + 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'.
-19000 + 800x + x2 = 0

Move the constant term to the right:

Add '19000' to each side of the equation.
-19000 + 800x + 19000 + x2 = 0 + 19000

Reorder the terms:
-19000 + 19000 + 800x + x2 = 0 + 19000

Combine like terms: -19000 + 19000 = 0
0 + 800x + x2 = 0 + 19000
800x + x2 = 0 + 19000

Combine like terms: 0 + 19000 = 19000
800x + x2 = 19000

The x term is 800x.  Take half its coefficient (400).
Square it (160000) and add it to both sides.

Add '160000' to each side of the equation.
800x + 160000 + x2 = 19000 + 160000

Reorder the terms:
160000 + 800x + x2 = 19000 + 160000

Combine like terms: 19000 + 160000 = 179000
160000 + 800x + x2 = 179000

Factor a perfect square on the left side:
(x + 400)(x + 400) = 179000

Calculate the square root of the right side: 423.083916026

Break this problem into two subproblems by setting 
(x + 400) equal to 423.083916026 and -423.083916026.


Subproblem 1
x + 400 = 423.083916026

Simplifying
x + 400 = 423.083916026

Reorder the terms:
400 + x = 423.083916026

Solving
400 + x = 423.083916026

Solving for variable 'x'.

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

Add '-400' to each side of the equation.
400 + -400 + x = 423.083916026 + -400

Combine like terms: 400 + -400 = 0
0 + x = 423.083916026 + -400
x = 423.083916026 + -400

Combine like terms: 423.083916026 + -400 = 23.083916026
x = 23.083916026

Simplifying
x = 23.083916026


Subproblem 2
x + 400 = -423.083916026

Simplifying
x + 400 = -423.083916026

Reorder the terms:
400 + x = -423.083916026

Solving
400 + x = -423.083916026

Solving for variable 'x'.

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

Add '-400' to each side of the equation.
400 + -400 + x = -423.083916026 + -400

Combine like terms: 400 + -400 = 0
0 + x = -423.083916026 + -400
x = -423.083916026 + -400

Combine like terms: -423.083916026 + -400 = -823.083916026
x = -823.083916026

Simplifying
x = -823.083916026


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.083916026, -823.083916026}

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