X^2+5.5X-20=0

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Solution for X^2+5.5X-20=0 equation: 


Simplifying
X2 + 5.5X + -20 = 0

Reorder the terms:
-20 + 5.5X + X2 = 0

Solving
-20 + 5.5X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 5.5X + 20 + X2 = 0 + 20

Reorder the terms:
-20 + 20 + 5.5X + X2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 5.5X + X2 = 0 + 20
5.5X + X2 = 0 + 20

Combine like terms: 0 + 20 = 20
5.5X + X2 = 20

The X term is 5.5X.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5X + 7.5625 + X2 = 20 + 7.5625

Reorder the terms:
7.5625 + 5.5X + X2 = 20 + 7.5625

Combine like terms: 20 + 7.5625 = 27.5625
7.5625 + 5.5X + X2 = 27.5625

Factor a perfect square on the left side:
(X + 2.75)(X + 2.75) = 27.5625

Calculate the square root of the right side: 5.25

Break this problem into two subproblems by setting 
(X + 2.75) equal to 5.25 and -5.25.


Subproblem 1
X + 2.75 = 5.25

Simplifying
X + 2.75 = 5.25

Reorder the terms:
2.75 + X = 5.25

Solving
2.75 + X = 5.25

Solving for variable 'X'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + X = 5.25 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + X = 5.25 + -2.75
X = 5.25 + -2.75

Combine like terms: 5.25 + -2.75 = 2.5
X = 2.5

Simplifying
X = 2.5


Subproblem 2
X + 2.75 = -5.25

Simplifying
X + 2.75 = -5.25

Reorder the terms:
2.75 + X = -5.25

Solving
2.75 + X = -5.25

Solving for variable 'X'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + X = -5.25 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + X = -5.25 + -2.75
X = -5.25 + -2.75

Combine like terms: -5.25 + -2.75 = -8
X = -8

Simplifying
X = -8


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.5, -8}

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