x^2-5x-1955=0

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Solution for x^2-5x-1955=0 equation: 


Simplifying
x2 + -5x + -1955 = 0

Reorder the terms:
-1955 + -5x + x2 = 0

Solving
-1955 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1955' to each side of the equation.
-1955 + -5x + 1955 + x2 = 0 + 1955

Reorder the terms:
-1955 + 1955 + -5x + x2 = 0 + 1955

Combine like terms: -1955 + 1955 = 0
0 + -5x + x2 = 0 + 1955
-5x + x2 = 0 + 1955

Combine like terms: 0 + 1955 = 1955
-5x + x2 = 1955

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 = 1955 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 1955 + 6.25

Combine like terms: 1955 + 6.25 = 1961.25
6.25 + -5x + x2 = 1961.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1961.25

Calculate the square root of the right side: 44.286002303

Break this problem into two subproblems by setting 
(x + -2.5) equal to 44.286002303 and -44.286002303.


Subproblem 1
x + -2.5 = 44.286002303

Simplifying
x + -2.5 = 44.286002303

Reorder the terms:
-2.5 + x = 44.286002303

Solving
-2.5 + x = 44.286002303

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 = 44.286002303 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 44.286002303 + 2.5
x = 44.286002303 + 2.5

Combine like terms: 44.286002303 + 2.5 = 46.786002303
x = 46.786002303

Simplifying
x = 46.786002303


Subproblem 2
x + -2.5 = -44.286002303

Simplifying
x + -2.5 = -44.286002303

Reorder the terms:
-2.5 + x = -44.286002303

Solving
-2.5 + x = -44.286002303

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 = -44.286002303 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -44.286002303 + 2.5
x = -44.286002303 + 2.5

Combine like terms: -44.286002303 + 2.5 = -41.786002303
x = -41.786002303

Simplifying
x = -41.786002303


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {46.786002303, -41.786002303}

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