14x^2-48x-18=0

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Solution for 14x^2-48x-18=0 equation: 


Simplifying
14x2 + -48x + -18 = 0

Reorder the terms:
-18 + -48x + 14x2 = 0

Solving
-18 + -48x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -24x + 7x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -24x + 7x2)' equal to zero and attempt to solve:

Simplifying
-9 + -24x + 7x2 = 0

Solving
-9 + -24x + 7x2 = 0

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

Divide each side by '7'.
-1.285714286 + -3.428571429x + x2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + -3.428571429x + 1.285714286 + x2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + -3.428571429x + x2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + -3.428571429x + x2 = 0 + 1.285714286
-3.428571429x + x2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
-3.428571429x + x2 = 1.285714286

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 = 1.285714286 + 2.938775513

Reorder the terms:
2.938775513 + -3.428571429x + x2 = 1.285714286 + 2.938775513

Combine like terms: 1.285714286 + 2.938775513 = 4.224489799
2.938775513 + -3.428571429x + x2 = 4.224489799

Factor a perfect square on the left side:
(x + -1.714285715)(x + -1.714285715) = 4.224489799

Calculate the square root of the right side: 2.055356368

Break this problem into two subproblems by setting 
(x + -1.714285715) equal to 2.055356368 and -2.055356368.


Subproblem 1
x + -1.714285715 = 2.055356368

Simplifying
x + -1.714285715 = 2.055356368

Reorder the terms:
-1.714285715 + x = 2.055356368

Solving
-1.714285715 + x = 2.055356368

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 = 2.055356368 + 1.714285715

Combine like terms: -1.714285715 + 1.714285715 = 0.000000000
0.000000000 + x = 2.055356368 + 1.714285715
x = 2.055356368 + 1.714285715

Combine like terms: 2.055356368 + 1.714285715 = 3.769642083
x = 3.769642083

Simplifying
x = 3.769642083


Subproblem 2
x + -1.714285715 = -2.055356368

Simplifying
x + -1.714285715 = -2.055356368

Reorder the terms:
-1.714285715 + x = -2.055356368

Solving
-1.714285715 + x = -2.055356368

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 = -2.055356368 + 1.714285715

Combine like terms: -1.714285715 + 1.714285715 = 0.000000000
0.000000000 + x = -2.055356368 + 1.714285715
x = -2.055356368 + 1.714285715

Combine like terms: -2.055356368 + 1.714285715 = -0.341070653
x = -0.341070653

Simplifying
x = -0.341070653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.769642083, -0.341070653}
Solution
x = {3.769642083, -0.341070653}

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