3x^2-38x-14=0

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Solution for 3x^2-38x-14=0 equation: 


Simplifying
3x2 + -38x + -14 = 0

Reorder the terms:
-14 + -38x + 3x2 = 0

Solving
-14 + -38x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-4.666666667 + -12.66666667x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + -12.66666667x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + -12.66666667x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + -12.66666667x + x2 = 0 + 4.666666667
-12.66666667x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
-12.66666667x + x2 = 4.666666667

The x term is -12.66666667x.  Take half its coefficient (-6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
-12.66666667x + 40.11111113 + x2 = 4.666666667 + 40.11111113

Reorder the terms:
40.11111113 + -12.66666667x + x2 = 4.666666667 + 40.11111113

Combine like terms: 4.666666667 + 40.11111113 = 44.777777797
40.11111113 + -12.66666667x + x2 = 44.777777797

Factor a perfect square on the left side:
(x + -6.333333335)(x + -6.333333335) = 44.777777797

Calculate the square root of the right side: 6.691619968

Break this problem into two subproblems by setting 
(x + -6.333333335) equal to 6.691619968 and -6.691619968.


Subproblem 1
x + -6.333333335 = 6.691619968

Simplifying
x + -6.333333335 = 6.691619968

Reorder the terms:
-6.333333335 + x = 6.691619968

Solving
-6.333333335 + x = 6.691619968

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = 6.691619968 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = 6.691619968 + 6.333333335
x = 6.691619968 + 6.333333335

Combine like terms: 6.691619968 + 6.333333335 = 13.024953303
x = 13.024953303

Simplifying
x = 13.024953303


Subproblem 2
x + -6.333333335 = -6.691619968

Simplifying
x + -6.333333335 = -6.691619968

Reorder the terms:
-6.333333335 + x = -6.691619968

Solving
-6.333333335 + x = -6.691619968

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = -6.691619968 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = -6.691619968 + 6.333333335
x = -6.691619968 + 6.333333335

Combine like terms: -6.691619968 + 6.333333335 = -0.358286633
x = -0.358286633

Simplifying
x = -0.358286633


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.024953303, -0.358286633}

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