x^2-11x-48=0

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Solution for x^2-11x-48=0 equation: 


Simplifying
x2 + -11x + -48 = 0

Reorder the terms:
-48 + -11x + x2 = 0

Solving
-48 + -11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -11x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + -11x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -11x + x2 = 0 + 48
-11x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
-11x + x2 = 48

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 = 48 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 48 + 30.25

Combine like terms: 48 + 30.25 = 78.25
30.25 + -11x + x2 = 78.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(x + -5.5) equal to 8.845903006 and -8.845903006.


Subproblem 1
x + -5.5 = 8.845903006

Simplifying
x + -5.5 = 8.845903006

Reorder the terms:
-5.5 + x = 8.845903006

Solving
-5.5 + x = 8.845903006

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 = 8.845903006 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 8.845903006 + 5.5
x = 8.845903006 + 5.5

Combine like terms: 8.845903006 + 5.5 = 14.345903006
x = 14.345903006

Simplifying
x = 14.345903006


Subproblem 2
x + -5.5 = -8.845903006

Simplifying
x + -5.5 = -8.845903006

Reorder the terms:
-5.5 + x = -8.845903006

Solving
-5.5 + x = -8.845903006

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 = -8.845903006 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -8.845903006 + 5.5
x = -8.845903006 + 5.5

Combine like terms: -8.845903006 + 5.5 = -3.345903006
x = -3.345903006

Simplifying
x = -3.345903006


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.345903006, -3.345903006}

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