3x^2-38x-59=0

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Solution for 3x^2-38x-59=0 equation: 


Simplifying
3x2 + -38x + -59 = 0

Reorder the terms:
-59 + -38x + 3x2 = 0

Solving
-59 + -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'.
-19.66666667 + -12.66666667x + x2 = 0

Move the constant term to the right:

Add '19.66666667' to each side of the equation.
-19.66666667 + -12.66666667x + 19.66666667 + x2 = 0 + 19.66666667

Reorder the terms:
-19.66666667 + 19.66666667 + -12.66666667x + x2 = 0 + 19.66666667

Combine like terms: -19.66666667 + 19.66666667 = 0.00000000
0.00000000 + -12.66666667x + x2 = 0 + 19.66666667
-12.66666667x + x2 = 0 + 19.66666667

Combine like terms: 0 + 19.66666667 = 19.66666667
-12.66666667x + x2 = 19.66666667

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 = 19.66666667 + 40.11111113

Reorder the terms:
40.11111113 + -12.66666667x + x2 = 19.66666667 + 40.11111113

Combine like terms: 19.66666667 + 40.11111113 = 59.7777778
40.11111113 + -12.66666667x + x2 = 59.7777778

Factor a perfect square on the left side:
(x + -6.333333335)(x + -6.333333335) = 59.7777778

Calculate the square root of the right side: 7.731609005

Break this problem into two subproblems by setting 
(x + -6.333333335) equal to 7.731609005 and -7.731609005.


Subproblem 1
x + -6.333333335 = 7.731609005

Simplifying
x + -6.333333335 = 7.731609005

Reorder the terms:
-6.333333335 + x = 7.731609005

Solving
-6.333333335 + x = 7.731609005

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 = 7.731609005 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = 7.731609005 + 6.333333335
x = 7.731609005 + 6.333333335

Combine like terms: 7.731609005 + 6.333333335 = 14.06494234
x = 14.06494234

Simplifying
x = 14.06494234


Subproblem 2
x + -6.333333335 = -7.731609005

Simplifying
x + -6.333333335 = -7.731609005

Reorder the terms:
-6.333333335 + x = -7.731609005

Solving
-6.333333335 + x = -7.731609005

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 = -7.731609005 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = -7.731609005 + 6.333333335
x = -7.731609005 + 6.333333335

Combine like terms: -7.731609005 + 6.333333335 = -1.39827567
x = -1.39827567

Simplifying
x = -1.39827567


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.06494234, -1.39827567}

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