x^2-5x-1100=0

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Solution for x^2-5x-1100=0 equation: 


Simplifying
x2 + -5x + -1100 = 0

Reorder the terms:
-1100 + -5x + x2 = 0

Solving
-1100 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1100' to each side of the equation.
-1100 + -5x + 1100 + x2 = 0 + 1100

Reorder the terms:
-1100 + 1100 + -5x + x2 = 0 + 1100

Combine like terms: -1100 + 1100 = 0
0 + -5x + x2 = 0 + 1100
-5x + x2 = 0 + 1100

Combine like terms: 0 + 1100 = 1100
-5x + x2 = 1100

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 1100 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 1100 + 6.25

Combine like terms: 1100 + 6.25 = 1106.25
6.25 + -5x + x2 = 1106.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1106.25

Calculate the square root of the right side: 33.260336739

Break this problem into two subproblems by setting 
(x + -2.5) equal to 33.260336739 and -33.260336739.


Subproblem 1
x + -2.5 = 33.260336739

Simplifying
x + -2.5 = 33.260336739

Reorder the terms:
-2.5 + x = 33.260336739

Solving
-2.5 + x = 33.260336739

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 33.260336739 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 33.260336739 + 2.5
x = 33.260336739 + 2.5

Combine like terms: 33.260336739 + 2.5 = 35.760336739
x = 35.760336739

Simplifying
x = 35.760336739


Subproblem 2
x + -2.5 = -33.260336739

Simplifying
x + -2.5 = -33.260336739

Reorder the terms:
-2.5 + x = -33.260336739

Solving
-2.5 + x = -33.260336739

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -33.260336739 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -33.260336739 + 2.5
x = -33.260336739 + 2.5

Combine like terms: -33.260336739 + 2.5 = -30.760336739
x = -30.760336739

Simplifying
x = -30.760336739


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.760336739, -30.760336739}

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