14x^2-48x-494=0

Solution for 14x^2-48x-494=0 equation:

Simplifying
14x2 + -48x + -494 = 0

Reorder the terms:
-494 + -48x + 14x2 = 0

Solving
-494 + -48x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-247 + -24x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-247 + -24x + 7x2)' equal to zero and attempt to solve:

Simplifying
-247 + -24x + 7x2 = 0

Solving
-247 + -24x + 7x2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-35.28571429 + -3.428571429x + x2 = 0

Move the constant term to the right:

Add '35.28571429' to each side of the equation.
-35.28571429 + -3.428571429x + 35.28571429 + x2 = 0 + 35.28571429

Reorder the terms:
-35.28571429 + 35.28571429 + -3.428571429x + x2 = 0 + 35.28571429

Combine like terms: -35.28571429 + 35.28571429 = 0.00000000
0.00000000 + -3.428571429x + x2 = 0 + 35.28571429
-3.428571429x + x2 = 0 + 35.28571429

Combine like terms: 0 + 35.28571429 = 35.28571429
-3.428571429x + x2 = 35.28571429

The x term is -3.428571429x.  Take half its coefficient (-1.714285715).
Square it (2.938775513) and add it to both sides.

Add '2.938775513' to each side of the equation.
-3.428571429x + 2.938775513 + x2 = 35.28571429 + 2.938775513

Reorder the terms:
2.938775513 + -3.428571429x + x2 = 35.28571429 + 2.938775513

Combine like terms: 35.28571429 + 2.938775513 = 38.224489803
2.938775513 + -3.428571429x + x2 = 38.224489803

Factor a perfect square on the left side:
(x + -1.714285715)(x + -1.714285715) = 38.224489803

Calculate the square root of the right side: 6.182595717

Break this problem into two subproblems by setting 
(x + -1.714285715) equal to 6.182595717 and -6.182595717.

Subproblem 1
x + -1.714285715 = 6.182595717

Simplifying
x + -1.714285715 = 6.182595717

Reorder the terms:
-1.714285715 + x = 6.182595717

Solving
-1.714285715 + x = 6.182595717

Solving for variable 'x'.

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

Add '1.714285715' to each side of the equation.
-1.714285715 + 1.714285715 + x = 6.182595717 + 1.714285715

Combine like terms: -1.714285715 + 1.714285715 = 0.000000000
0.000000000 + x = 6.182595717 + 1.714285715
x = 6.182595717 + 1.714285715

Combine like terms: 6.182595717 + 1.714285715 = 7.896881432
x = 7.896881432

Simplifying
x = 7.896881432

Subproblem 2
x + -1.714285715 = -6.182595717

Simplifying
x + -1.714285715 = -6.182595717

Reorder the terms:
-1.714285715 + x = -6.182595717

Solving
-1.714285715 + x = -6.182595717

Solving for variable 'x'.

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

Add '1.714285715' to each side of the equation.
-1.714285715 + 1.714285715 + x = -6.182595717 + 1.714285715

Combine like terms: -1.714285715 + 1.714285715 = 0.000000000
0.000000000 + x = -6.182595717 + 1.714285715
x = -6.182595717 + 1.714285715

Combine like terms: -6.182595717 + 1.714285715 = -4.468310002
x = -4.468310002

Simplifying
x = -4.468310002

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.896881432, -4.468310002}
Solution
x = {7.896881432, -4.468310002}