3x^2-13x-37=0

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Solution for 3x^2-13x-37=0 equation: 


Simplifying
3x2 + -13x + -37 = 0

Reorder the terms:
-37 + -13x + 3x2 = 0

Solving
-37 + -13x + 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'.
-12.33333333 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '12.33333333' to each side of the equation.
-12.33333333 + -4.333333333x + 12.33333333 + x2 = 0 + 12.33333333

Reorder the terms:
-12.33333333 + 12.33333333 + -4.333333333x + x2 = 0 + 12.33333333

Combine like terms: -12.33333333 + 12.33333333 = 0.00000000
0.00000000 + -4.333333333x + x2 = 0 + 12.33333333
-4.333333333x + x2 = 0 + 12.33333333

Combine like terms: 0 + 12.33333333 = 12.33333333
-4.333333333x + x2 = 12.33333333

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = 12.33333333 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = 12.33333333 + 4.694444446

Combine like terms: 12.33333333 + 4.694444446 = 17.027777776
4.694444446 + -4.333333333x + x2 = 17.027777776

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 17.027777776

Calculate the square root of the right side: 4.126472801

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 4.126472801 and -4.126472801.


Subproblem 1
x + -2.166666667 = 4.126472801

Simplifying
x + -2.166666667 = 4.126472801

Reorder the terms:
-2.166666667 + x = 4.126472801

Solving
-2.166666667 + x = 4.126472801

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 4.126472801 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 4.126472801 + 2.166666667
x = 4.126472801 + 2.166666667

Combine like terms: 4.126472801 + 2.166666667 = 6.293139468
x = 6.293139468

Simplifying
x = 6.293139468


Subproblem 2
x + -2.166666667 = -4.126472801

Simplifying
x + -2.166666667 = -4.126472801

Reorder the terms:
-2.166666667 + x = -4.126472801

Solving
-2.166666667 + x = -4.126472801

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -4.126472801 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -4.126472801 + 2.166666667
x = -4.126472801 + 2.166666667

Combine like terms: -4.126472801 + 2.166666667 = -1.959806134
x = -1.959806134

Simplifying
x = -1.959806134


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.293139468, -1.959806134}

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