0.045X^2-103X-140000=0

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Solution for 0.045X^2-103X-140000=0 equation: 


Simplifying
0.045X2 + -103X + -140000 = 0

Reorder the terms:
-140000 + -103X + 0.045X2 = 0

Solving
-140000 + -103X + 0.045X2 = 0

Solving for variable 'X'.

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

Divide each side by '0.045'.
-3111111.111 + -2288.888889X + X2 = 0

Move the constant term to the right:

Add '3111111.111' to each side of the equation.
-3111111.111 + -2288.888889X + 3111111.111 + X2 = 0 + 3111111.111

Reorder the terms:
-3111111.111 + 3111111.111 + -2288.888889X + X2 = 0 + 3111111.111

Combine like terms: -3111111.111 + 3111111.111 = 0.000
0.000 + -2288.888889X + X2 = 0 + 3111111.111
-2288.888889X + X2 = 0 + 3111111.111

Combine like terms: 0 + 3111111.111 = 3111111.111
-2288.888889X + X2 = 3111111.111

The X term is -2288.888889X.  Take half its coefficient (-1144.444445).
Square it (1309753.088) and add it to both sides.

Add '1309753.088' to each side of the equation.
-2288.888889X + 1309753.088 + X2 = 3111111.111 + 1309753.088

Reorder the terms:
1309753.088 + -2288.888889X + X2 = 3111111.111 + 1309753.088

Combine like terms: 3111111.111 + 1309753.088 = 4420864.199
1309753.088 + -2288.888889X + X2 = 4420864.199

Factor a perfect square on the left side:
(X + -1144.444445)(X + -1144.444445) = 4420864.199

Calculate the square root of the right side: 2102.58512289

Break this problem into two subproblems by setting 
(X + -1144.444445) equal to 2102.58512289 and -2102.58512289.


Subproblem 1
X + -1144.444445 = 2102.58512289

Simplifying
X + -1144.444445 = 2102.58512289

Reorder the terms:
-1144.444445 + X = 2102.58512289

Solving
-1144.444445 + X = 2102.58512289

Solving for variable 'X'.

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

Add '1144.444445' to each side of the equation.
-1144.444445 + 1144.444445 + X = 2102.58512289 + 1144.444445

Combine like terms: -1144.444445 + 1144.444445 = 0.000000
0.000000 + X = 2102.58512289 + 1144.444445
X = 2102.58512289 + 1144.444445

Combine like terms: 2102.58512289 + 1144.444445 = 3247.02956789
X = 3247.02956789

Simplifying
X = 3247.02956789


Subproblem 2
X + -1144.444445 = -2102.58512289

Simplifying
X + -1144.444445 = -2102.58512289

Reorder the terms:
-1144.444445 + X = -2102.58512289

Solving
-1144.444445 + X = -2102.58512289

Solving for variable 'X'.

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

Add '1144.444445' to each side of the equation.
-1144.444445 + 1144.444445 + X = -2102.58512289 + 1144.444445

Combine like terms: -1144.444445 + 1144.444445 = 0.000000
0.000000 + X = -2102.58512289 + 1144.444445
X = -2102.58512289 + 1144.444445

Combine like terms: -2102.58512289 + 1144.444445 = -958.14067789
X = -958.14067789

Simplifying
X = -958.14067789


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {3247.02956789, -958.14067789}

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