x^2+105x-140000=0

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Solution for x^2+105x-140000=0 equation: 


Simplifying
x2 + 105x + -140000 = 0

Reorder the terms:
-140000 + 105x + x2 = 0

Solving
-140000 + 105x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '140000' to each side of the equation.
-140000 + 105x + 140000 + x2 = 0 + 140000

Reorder the terms:
-140000 + 140000 + 105x + x2 = 0 + 140000

Combine like terms: -140000 + 140000 = 0
0 + 105x + x2 = 0 + 140000
105x + x2 = 0 + 140000

Combine like terms: 0 + 140000 = 140000
105x + x2 = 140000

The x term is 105x.  Take half its coefficient (52.5).
Square it (2756.25) and add it to both sides.

Add '2756.25' to each side of the equation.
105x + 2756.25 + x2 = 140000 + 2756.25

Reorder the terms:
2756.25 + 105x + x2 = 140000 + 2756.25

Combine like terms: 140000 + 2756.25 = 142756.25
2756.25 + 105x + x2 = 142756.25

Factor a perfect square on the left side:
(x + 52.5)(x + 52.5) = 142756.25

Calculate the square root of the right side: 377.830980731

Break this problem into two subproblems by setting 
(x + 52.5) equal to 377.830980731 and -377.830980731.


Subproblem 1
x + 52.5 = 377.830980731

Simplifying
x + 52.5 = 377.830980731

Reorder the terms:
52.5 + x = 377.830980731

Solving
52.5 + x = 377.830980731

Solving for variable 'x'.

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

Add '-52.5' to each side of the equation.
52.5 + -52.5 + x = 377.830980731 + -52.5

Combine like terms: 52.5 + -52.5 = 0.0
0.0 + x = 377.830980731 + -52.5
x = 377.830980731 + -52.5

Combine like terms: 377.830980731 + -52.5 = 325.330980731
x = 325.330980731

Simplifying
x = 325.330980731


Subproblem 2
x + 52.5 = -377.830980731

Simplifying
x + 52.5 = -377.830980731

Reorder the terms:
52.5 + x = -377.830980731

Solving
52.5 + x = -377.830980731

Solving for variable 'x'.

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

Add '-52.5' to each side of the equation.
52.5 + -52.5 + x = -377.830980731 + -52.5

Combine like terms: 52.5 + -52.5 = 0.0
0.0 + x = -377.830980731 + -52.5
x = -377.830980731 + -52.5

Combine like terms: -377.830980731 + -52.5 = -430.330980731
x = -430.330980731

Simplifying
x = -430.330980731


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {325.330980731, -430.330980731}

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