X^2+11X-38.25=0

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Solution for X^2+11X-38.25=0 equation: 


Simplifying
X2 + 11X + -38.25 = 0

Reorder the terms:
-38.25 + 11X + X2 = 0

Solving
-38.25 + 11X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '38.25' to each side of the equation.
-38.25 + 11X + 38.25 + X2 = 0 + 38.25

Reorder the terms:
-38.25 + 38.25 + 11X + X2 = 0 + 38.25

Combine like terms: -38.25 + 38.25 = 0.00
0.00 + 11X + X2 = 0 + 38.25
11X + X2 = 0 + 38.25

Combine like terms: 0 + 38.25 = 38.25
11X + X2 = 38.25

The X term is 11X.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11X + 30.25 + X2 = 38.25 + 30.25

Reorder the terms:
30.25 + 11X + X2 = 38.25 + 30.25

Combine like terms: 38.25 + 30.25 = 68.5
30.25 + 11X + X2 = 68.5

Factor a perfect square on the left side:
(X + 5.5)(X + 5.5) = 68.5

Calculate the square root of the right side: 8.276472679

Break this problem into two subproblems by setting 
(X + 5.5) equal to 8.276472679 and -8.276472679.


Subproblem 1
X + 5.5 = 8.276472679

Simplifying
X + 5.5 = 8.276472679

Reorder the terms:
5.5 + X = 8.276472679

Solving
5.5 + X = 8.276472679

Solving for variable 'X'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + X = 8.276472679 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + X = 8.276472679 + -5.5
X = 8.276472679 + -5.5

Combine like terms: 8.276472679 + -5.5 = 2.776472679
X = 2.776472679

Simplifying
X = 2.776472679


Subproblem 2
X + 5.5 = -8.276472679

Simplifying
X + 5.5 = -8.276472679

Reorder the terms:
5.5 + X = -8.276472679

Solving
5.5 + X = -8.276472679

Solving for variable 'X'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + X = -8.276472679 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + X = -8.276472679 + -5.5
X = -8.276472679 + -5.5

Combine like terms: -8.276472679 + -5.5 = -13.776472679
X = -13.776472679

Simplifying
X = -13.776472679


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.776472679, -13.776472679}

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