3x^2-5x-59=0

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Solution for 3x^2-5x-59=0 equation: 


Simplifying
3x2 + -5x + -59 = 0

Reorder the terms:
-59 + -5x + 3x2 = 0

Solving
-59 + -5x + 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 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '19.66666667' to each side of the equation.
-19.66666667 + -1.666666667x + 19.66666667 + x2 = 0 + 19.66666667

Reorder the terms:
-19.66666667 + 19.66666667 + -1.666666667x + x2 = 0 + 19.66666667

Combine like terms: -19.66666667 + 19.66666667 = 0.00000000
0.00000000 + -1.666666667x + x2 = 0 + 19.66666667
-1.666666667x + x2 = 0 + 19.66666667

Combine like terms: 0 + 19.66666667 = 19.66666667
-1.666666667x + x2 = 19.66666667

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 19.66666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 19.66666667 + 0.6944444447

Combine like terms: 19.66666667 + 0.6944444447 = 20.3611111147
0.6944444447 + -1.666666667x + x2 = 20.3611111147

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 20.3611111147

Calculate the square root of the right side: 4.512328791

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 4.512328791 and -4.512328791.


Subproblem 1
x + -0.8333333335 = 4.512328791

Simplifying
x + -0.8333333335 = 4.512328791

Reorder the terms:
-0.8333333335 + x = 4.512328791

Solving
-0.8333333335 + x = 4.512328791

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 4.512328791 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 4.512328791 + 0.8333333335
x = 4.512328791 + 0.8333333335

Combine like terms: 4.512328791 + 0.8333333335 = 5.3456621245
x = 5.3456621245

Simplifying
x = 5.3456621245


Subproblem 2
x + -0.8333333335 = -4.512328791

Simplifying
x + -0.8333333335 = -4.512328791

Reorder the terms:
-0.8333333335 + x = -4.512328791

Solving
-0.8333333335 + x = -4.512328791

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -4.512328791 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -4.512328791 + 0.8333333335
x = -4.512328791 + 0.8333333335

Combine like terms: -4.512328791 + 0.8333333335 = -3.6789954575
x = -3.6789954575

Simplifying
x = -3.6789954575


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.3456621245, -3.6789954575}

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