x^2+5x-2200=0

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Solution for x^2+5x-2200=0 equation: 


Simplifying
x2 + 5x + -2200 = 0

Reorder the terms:
-2200 + 5x + x2 = 0

Solving
-2200 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2200' to each side of the equation.
-2200 + 5x + 2200 + x2 = 0 + 2200

Reorder the terms:
-2200 + 2200 + 5x + x2 = 0 + 2200

Combine like terms: -2200 + 2200 = 0
0 + 5x + x2 = 0 + 2200
5x + x2 = 0 + 2200

Combine like terms: 0 + 2200 = 2200
5x + x2 = 2200

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 = 2200 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2200 + 6.25

Combine like terms: 2200 + 6.25 = 2206.25
6.25 + 5x + x2 = 2206.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 2206.25

Calculate the square root of the right side: 46.97073557

Break this problem into two subproblems by setting 
(x + 2.5) equal to 46.97073557 and -46.97073557.


Subproblem 1
x + 2.5 = 46.97073557

Simplifying
x + 2.5 = 46.97073557

Reorder the terms:
2.5 + x = 46.97073557

Solving
2.5 + x = 46.97073557

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 = 46.97073557 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 46.97073557 + -2.5
x = 46.97073557 + -2.5

Combine like terms: 46.97073557 + -2.5 = 44.47073557
x = 44.47073557

Simplifying
x = 44.47073557


Subproblem 2
x + 2.5 = -46.97073557

Simplifying
x + 2.5 = -46.97073557

Reorder the terms:
2.5 + x = -46.97073557

Solving
2.5 + x = -46.97073557

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 = -46.97073557 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -46.97073557 + -2.5
x = -46.97073557 + -2.5

Combine like terms: -46.97073557 + -2.5 = -49.47073557
x = -49.47073557

Simplifying
x = -49.47073557


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {44.47073557, -49.47073557}

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