3x^2-19x-36=0

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Solution for 3x^2-19x-36=0 equation: 


Simplifying
3x2 + -19x + -36 = 0

Reorder the terms:
-36 + -19x + 3x2 = 0

Solving
-36 + -19x + 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 + -6.333333333x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -6.333333333x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -6.333333333x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -6.333333333x + x2 = 0 + 12
-6.333333333x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-6.333333333x + x2 = 12

The x term is -6.333333333x.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333x + 10.02777778 + x2 = 12 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333x + x2 = 12 + 10.02777778

Combine like terms: 12 + 10.02777778 = 22.02777778
10.02777778 + -6.333333333x + x2 = 22.02777778

Factor a perfect square on the left side:
(x + -3.166666667)(x + -3.166666667) = 22.02777778

Calculate the square root of the right side: 4.693375947

Break this problem into two subproblems by setting 
(x + -3.166666667) equal to 4.693375947 and -4.693375947.


Subproblem 1
x + -3.166666667 = 4.693375947

Simplifying
x + -3.166666667 = 4.693375947

Reorder the terms:
-3.166666667 + x = 4.693375947

Solving
-3.166666667 + x = 4.693375947

Solving for variable 'x'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = 4.693375947 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = 4.693375947 + 3.166666667
x = 4.693375947 + 3.166666667

Combine like terms: 4.693375947 + 3.166666667 = 7.860042614
x = 7.860042614

Simplifying
x = 7.860042614


Subproblem 2
x + -3.166666667 = -4.693375947

Simplifying
x + -3.166666667 = -4.693375947

Reorder the terms:
-3.166666667 + x = -4.693375947

Solving
-3.166666667 + x = -4.693375947

Solving for variable 'x'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = -4.693375947 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = -4.693375947 + 3.166666667
x = -4.693375947 + 3.166666667

Combine like terms: -4.693375947 + 3.166666667 = -1.52670928
x = -1.52670928

Simplifying
x = -1.52670928


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.860042614, -1.52670928}

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