x^2-11x-40=0

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Solution for x^2-11x-40=0 equation: 


Simplifying
x2 + -11x + -40 = 0

Reorder the terms:
-40 + -11x + x2 = 0

Solving
-40 + -11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -11x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -11x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -11x + x2 = 0 + 40
-11x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-11x + x2 = 40

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 = 40 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 40 + 30.25

Combine like terms: 40 + 30.25 = 70.25
30.25 + -11x + x2 = 70.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(x + -5.5) equal to 8.381527307 and -8.381527307.


Subproblem 1
x + -5.5 = 8.381527307

Simplifying
x + -5.5 = 8.381527307

Reorder the terms:
-5.5 + x = 8.381527307

Solving
-5.5 + x = 8.381527307

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 = 8.381527307 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 8.381527307 + 5.5
x = 8.381527307 + 5.5

Combine like terms: 8.381527307 + 5.5 = 13.881527307
x = 13.881527307

Simplifying
x = 13.881527307


Subproblem 2
x + -5.5 = -8.381527307

Simplifying
x + -5.5 = -8.381527307

Reorder the terms:
-5.5 + x = -8.381527307

Solving
-5.5 + x = -8.381527307

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 = -8.381527307 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -8.381527307 + 5.5
x = -8.381527307 + 5.5

Combine like terms: -8.381527307 + 5.5 = -2.881527307
x = -2.881527307

Simplifying
x = -2.881527307


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.881527307, -2.881527307}

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