0=x^2+111x-104000

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Solution for 0=x^2+111x-104000 equation:


Simplifying
0 = x2 + 111x + -104000

Reorder the terms:
0 = -104000 + 111x + x2

Solving
0 = -104000 + 111x + x2

Solving for variable 'x'.

Combine like terms: 0 + 104000 = 104000
104000 + -111x + -1x2 = -104000 + 111x + x2 + 104000 + -111x + -1x2

Reorder the terms:
104000 + -111x + -1x2 = -104000 + 104000 + 111x + -111x + x2 + -1x2

Combine like terms: -104000 + 104000 = 0
104000 + -111x + -1x2 = 0 + 111x + -111x + x2 + -1x2
104000 + -111x + -1x2 = 111x + -111x + x2 + -1x2

Combine like terms: 111x + -111x = 0
104000 + -111x + -1x2 = 0 + x2 + -1x2
104000 + -111x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
104000 + -111x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-104000 + 111x + x2 = 0

Move the constant term to the right:

Add '104000' to each side of the equation.
-104000 + 111x + 104000 + x2 = 0 + 104000

Reorder the terms:
-104000 + 104000 + 111x + x2 = 0 + 104000

Combine like terms: -104000 + 104000 = 0
0 + 111x + x2 = 0 + 104000
111x + x2 = 0 + 104000

Combine like terms: 0 + 104000 = 104000
111x + x2 = 104000

The x term is 111x.  Take half its coefficient (55.5).
Square it (3080.25) and add it to both sides.

Add '3080.25' to each side of the equation.
111x + 3080.25 + x2 = 104000 + 3080.25

Reorder the terms:
3080.25 + 111x + x2 = 104000 + 3080.25

Combine like terms: 104000 + 3080.25 = 107080.25
3080.25 + 111x + x2 = 107080.25

Factor a perfect square on the left side:
(x + 55.5)(x + 55.5) = 107080.25

Calculate the square root of the right side: 327.231187389

Break this problem into two subproblems by setting 
(x + 55.5) equal to 327.231187389 and -327.231187389.

Subproblem 1

x + 55.5 = 327.231187389 Simplifying x + 55.5 = 327.231187389 Reorder the terms: 55.5 + x = 327.231187389 Solving 55.5 + x = 327.231187389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55.5' to each side of the equation. 55.5 + -55.5 + x = 327.231187389 + -55.5 Combine like terms: 55.5 + -55.5 = 0.0 0.0 + x = 327.231187389 + -55.5 x = 327.231187389 + -55.5 Combine like terms: 327.231187389 + -55.5 = 271.731187389 x = 271.731187389 Simplifying x = 271.731187389

Subproblem 2

x + 55.5 = -327.231187389 Simplifying x + 55.5 = -327.231187389 Reorder the terms: 55.5 + x = -327.231187389 Solving 55.5 + x = -327.231187389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55.5' to each side of the equation. 55.5 + -55.5 + x = -327.231187389 + -55.5 Combine like terms: 55.5 + -55.5 = 0.0 0.0 + x = -327.231187389 + -55.5 x = -327.231187389 + -55.5 Combine like terms: -327.231187389 + -55.5 = -382.731187389 x = -382.731187389 Simplifying x = -382.731187389

Solution

The solution to the problem is based on the solutions from the subproblems. x = {271.731187389, -382.731187389}

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