x^2-6x-48=0

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Solution for x^2-6x-48=0 equation:


Simplifying
x2 + -6x + -48 = 0

Reorder the terms:
-48 + -6x + x2 = 0

Solving
-48 + -6x + 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 + -6x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + -6x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -6x + x2 = 0 + 48
-6x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
-6x + x2 = 48

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 48 + 9

Reorder the terms:
9 + -6x + x2 = 48 + 9

Combine like terms: 48 + 9 = 57
9 + -6x + x2 = 57

Factor a perfect square on the left side:
(x + -3)(x + -3) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + -3) equal to 7.549834435 and -7.549834435.


Subproblem 1
x + -3 = 7.549834435

Simplifying
x + -3 = 7.549834435

Reorder the terms:
-3 + x = 7.549834435

Solving
-3 + x = 7.549834435

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 7.549834435 + 3

Combine like terms: -3 + 3 = 0
0 + x = 7.549834435 + 3
x = 7.549834435 + 3

Combine like terms: 7.549834435 + 3 = 10.549834435
x = 10.549834435

Simplifying
x = 10.549834435


Subproblem 2
x + -3 = -7.549834435

Simplifying
x + -3 = -7.549834435

Reorder the terms:
-3 + x = -7.549834435

Solving
-3 + x = -7.549834435

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -7.549834435 + 3

Combine like terms: -3 + 3 = 0
0 + x = -7.549834435 + 3
x = -7.549834435 + 3

Combine like terms: -7.549834435 + 3 = -4.549834435
x = -4.549834435

Simplifying
x = -4.549834435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.549834435, -4.549834435}

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