x^2-10x-48=0

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Solution for x^2-10x-48=0 equation: 


Simplifying
x2 + -10x + -48 = 0

Reorder the terms:
-48 + -10x + x2 = 0

Solving
-48 + -10x + 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 + -10x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + -10x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -10x + x2 = 0 + 48
-10x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
-10x + x2 = 48

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 48 + 25

Reorder the terms:
25 + -10x + x2 = 48 + 25

Combine like terms: 48 + 25 = 73
25 + -10x + x2 = 73

Factor a perfect square on the left side:
(x + -5)(x + -5) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(x + -5) equal to 8.544003745 and -8.544003745.


Subproblem 1
x + -5 = 8.544003745

Simplifying
x + -5 = 8.544003745

Reorder the terms:
-5 + x = 8.544003745

Solving
-5 + x = 8.544003745

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 8.544003745 + 5

Combine like terms: -5 + 5 = 0
0 + x = 8.544003745 + 5
x = 8.544003745 + 5

Combine like terms: 8.544003745 + 5 = 13.544003745
x = 13.544003745

Simplifying
x = 13.544003745


Subproblem 2
x + -5 = -8.544003745

Simplifying
x + -5 = -8.544003745

Reorder the terms:
-5 + x = -8.544003745

Solving
-5 + x = -8.544003745

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -8.544003745 + 5

Combine like terms: -5 + 5 = 0
0 + x = -8.544003745 + 5
x = -8.544003745 + 5

Combine like terms: -8.544003745 + 5 = -3.544003745
x = -3.544003745

Simplifying
x = -3.544003745


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.544003745, -3.544003745}

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