-0.00008x^2+0.199x-73.944=0

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Solution for -0.00008x^2+0.199x-73.944=0 equation: 


Simplifying
-0.00008x2 + 0.199x + -73.944 = 0

Reorder the terms:
-73.944 + 0.199x + -0.00008x2 = 0

Solving
-73.944 + 0.199x + -0.00008x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.00008 the coefficient of the squared term: 

Divide each side by '-0.00008'.
924300 + -2487.5x + x2 = 0

Move the constant term to the right:

Add '-924300' to each side of the equation.
924300 + -2487.5x + -924300 + x2 = 0 + -924300

Reorder the terms:
924300 + -924300 + -2487.5x + x2 = 0 + -924300

Combine like terms: 924300 + -924300 = 0
0 + -2487.5x + x2 = 0 + -924300
-2487.5x + x2 = 0 + -924300

Combine like terms: 0 + -924300 = -924300
-2487.5x + x2 = -924300

The x term is -2487.5x.  Take half its coefficient (-1243.75).
Square it (1546914.063) and add it to both sides.

Add '1546914.063' to each side of the equation.
-2487.5x + 1546914.063 + x2 = -924300 + 1546914.063

Reorder the terms:
1546914.063 + -2487.5x + x2 = -924300 + 1546914.063

Combine like terms: -924300 + 1546914.063 = 622614.063
1546914.063 + -2487.5x + x2 = 622614.063

Factor a perfect square on the left side:
(x + -1243.75)(x + -1243.75) = 622614.063

Calculate the square root of the right side: 789.058973081

Break this problem into two subproblems by setting 
(x + -1243.75) equal to 789.058973081 and -789.058973081.


Subproblem 1
x + -1243.75 = 789.058973081

Simplifying
x + -1243.75 = 789.058973081

Reorder the terms:
-1243.75 + x = 789.058973081

Solving
-1243.75 + x = 789.058973081

Solving for variable 'x'.

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

Add '1243.75' to each side of the equation.
-1243.75 + 1243.75 + x = 789.058973081 + 1243.75

Combine like terms: -1243.75 + 1243.75 = 0.00
0.00 + x = 789.058973081 + 1243.75
x = 789.058973081 + 1243.75

Combine like terms: 789.058973081 + 1243.75 = 2032.808973081
x = 2032.808973081

Simplifying
x = 2032.808973081


Subproblem 2
x + -1243.75 = -789.058973081

Simplifying
x + -1243.75 = -789.058973081

Reorder the terms:
-1243.75 + x = -789.058973081

Solving
-1243.75 + x = -789.058973081

Solving for variable 'x'.

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

Add '1243.75' to each side of the equation.
-1243.75 + 1243.75 + x = -789.058973081 + 1243.75

Combine like terms: -1243.75 + 1243.75 = 0.00
0.00 + x = -789.058973081 + 1243.75
x = -789.058973081 + 1243.75

Combine like terms: -789.058973081 + 1243.75 = 454.691026919
x = 454.691026919

Simplifying
x = 454.691026919


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2032.808973081, 454.691026919}

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