X^2+11X-150=0

Solution for X^2+11X-150=0 equation:

Simplifying
X2 + 11X + -150 = 0

Reorder the terms:
-150 + 11X + X2 = 0

Solving
-150 + 11X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '150' to each side of the equation.
-150 + 11X + 150 + X2 = 0 + 150

Reorder the terms:
-150 + 150 + 11X + X2 = 0 + 150

Combine like terms: -150 + 150 = 0
0 + 11X + X2 = 0 + 150
11X + X2 = 0 + 150

Combine like terms: 0 + 150 = 150
11X + X2 = 150

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 = 150 + 30.25

Reorder the terms:
30.25 + 11X + X2 = 150 + 30.25

Combine like terms: 150 + 30.25 = 180.25
30.25 + 11X + X2 = 180.25

Factor a perfect square on the left side:
(X + 5.5)(X + 5.5) = 180.25

Calculate the square root of the right side: 13.425721582

Break this problem into two subproblems by setting 
(X + 5.5) equal to 13.425721582 and -13.425721582.

Subproblem 1
X + 5.5 = 13.425721582

Simplifying
X + 5.5 = 13.425721582

Reorder the terms:
5.5 + X = 13.425721582

Solving
5.5 + X = 13.425721582

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 = 13.425721582 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + X = 13.425721582 + -5.5
X = 13.425721582 + -5.5

Combine like terms: 13.425721582 + -5.5 = 7.925721582
X = 7.925721582

Simplifying
X = 7.925721582

Subproblem 2
X + 5.5 = -13.425721582

Simplifying
X + 5.5 = -13.425721582

Reorder the terms:
5.5 + X = -13.425721582

Solving
5.5 + X = -13.425721582

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 = -13.425721582 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + X = -13.425721582 + -5.5
X = -13.425721582 + -5.5

Combine like terms: -13.425721582 + -5.5 = -18.925721582
X = -18.925721582

Simplifying
X = -18.925721582

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {7.925721582, -18.925721582}