X^2+X-19.11=0

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Solution for X^2+X-19.11=0 equation: 


Simplifying
X2 + X + -19.11 = 0

Reorder the terms:
-19.11 + X + X2 = 0

Solving
-19.11 + X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '19.11' to each side of the equation.
-19.11 + X + 19.11 + X2 = 0 + 19.11

Reorder the terms:
-19.11 + 19.11 + X + X2 = 0 + 19.11

Combine like terms: -19.11 + 19.11 = 0.00
0.00 + X + X2 = 0 + 19.11
X + X2 = 0 + 19.11

Combine like terms: 0 + 19.11 = 19.11
X + X2 = 19.11

The X term is X.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
X + 0.25 + X2 = 19.11 + 0.25

Reorder the terms:
0.25 + X + X2 = 19.11 + 0.25

Combine like terms: 19.11 + 0.25 = 19.36
0.25 + X + X2 = 19.36

Factor a perfect square on the left side:
(X + 0.5)(X + 0.5) = 19.36

Calculate the square root of the right side: 4.4

Break this problem into two subproblems by setting 
(X + 0.5) equal to 4.4 and -4.4.


Subproblem 1
X + 0.5 = 4.4

Simplifying
X + 0.5 = 4.4

Reorder the terms:
0.5 + X = 4.4

Solving
0.5 + X = 4.4

Solving for variable 'X'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + X = 4.4 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = 4.4 + -0.5
X = 4.4 + -0.5

Combine like terms: 4.4 + -0.5 = 3.9
X = 3.9

Simplifying
X = 3.9


Subproblem 2
X + 0.5 = -4.4

Simplifying
X + 0.5 = -4.4

Reorder the terms:
0.5 + X = -4.4

Solving
0.5 + X = -4.4

Solving for variable 'X'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + X = -4.4 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = -4.4 + -0.5
X = -4.4 + -0.5

Combine like terms: -4.4 + -0.5 = -4.9
X = -4.9

Simplifying
X = -4.9


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {3.9, -4.9}

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