x^2+110x-2000=0

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Solution for x^2+110x-2000=0 equation: 


Simplifying
x2 + 110x + -2000 = 0

Reorder the terms:
-2000 + 110x + x2 = 0

Solving
-2000 + 110x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2000' to each side of the equation.
-2000 + 110x + 2000 + x2 = 0 + 2000

Reorder the terms:
-2000 + 2000 + 110x + x2 = 0 + 2000

Combine like terms: -2000 + 2000 = 0
0 + 110x + x2 = 0 + 2000
110x + x2 = 0 + 2000

Combine like terms: 0 + 2000 = 2000
110x + x2 = 2000

The x term is 110x.  Take half its coefficient (55).
Square it (3025) and add it to both sides.

Add '3025' to each side of the equation.
110x + 3025 + x2 = 2000 + 3025

Reorder the terms:
3025 + 110x + x2 = 2000 + 3025

Combine like terms: 2000 + 3025 = 5025
3025 + 110x + x2 = 5025

Factor a perfect square on the left side:
(x + 55)(x + 55) = 5025

Calculate the square root of the right side: 70.887234394

Break this problem into two subproblems by setting 
(x + 55) equal to 70.887234394 and -70.887234394.


Subproblem 1
x + 55 = 70.887234394

Simplifying
x + 55 = 70.887234394

Reorder the terms:
55 + x = 70.887234394

Solving
55 + x = 70.887234394

Solving for variable 'x'.

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

Add '-55' to each side of the equation.
55 + -55 + x = 70.887234394 + -55

Combine like terms: 55 + -55 = 0
0 + x = 70.887234394 + -55
x = 70.887234394 + -55

Combine like terms: 70.887234394 + -55 = 15.887234394
x = 15.887234394

Simplifying
x = 15.887234394


Subproblem 2
x + 55 = -70.887234394

Simplifying
x + 55 = -70.887234394

Reorder the terms:
55 + x = -70.887234394

Solving
55 + x = -70.887234394

Solving for variable 'x'.

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

Add '-55' to each side of the equation.
55 + -55 + x = -70.887234394 + -55

Combine like terms: 55 + -55 = 0
0 + x = -70.887234394 + -55
x = -70.887234394 + -55

Combine like terms: -70.887234394 + -55 = -125.887234394
x = -125.887234394

Simplifying
x = -125.887234394


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.887234394, -125.887234394}

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