3x^2-22x-72=0

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Solution for 3x^2-22x-72=0 equation: 


Simplifying
3x2 + -22x + -72 = 0

Reorder the terms:
-72 + -22x + 3x2 = 0

Solving
-72 + -22x + 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'.
-24 + -7.333333333x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -7.333333333x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -7.333333333x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -7.333333333x + x2 = 0 + 24
-7.333333333x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-7.333333333x + x2 = 24

The x term is -7.333333333x.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333x + 13.44444445 + x2 = 24 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333x + x2 = 24 + 13.44444445

Combine like terms: 24 + 13.44444445 = 37.44444445
13.44444445 + -7.333333333x + x2 = 37.44444445

Factor a perfect square on the left side:
(x + -3.666666667)(x + -3.666666667) = 37.44444445

Calculate the square root of the right side: 6.119186584

Break this problem into two subproblems by setting 
(x + -3.666666667) equal to 6.119186584 and -6.119186584.


Subproblem 1
x + -3.666666667 = 6.119186584

Simplifying
x + -3.666666667 = 6.119186584

Reorder the terms:
-3.666666667 + x = 6.119186584

Solving
-3.666666667 + x = 6.119186584

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = 6.119186584 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = 6.119186584 + 3.666666667
x = 6.119186584 + 3.666666667

Combine like terms: 6.119186584 + 3.666666667 = 9.785853251
x = 9.785853251

Simplifying
x = 9.785853251


Subproblem 2
x + -3.666666667 = -6.119186584

Simplifying
x + -3.666666667 = -6.119186584

Reorder the terms:
-3.666666667 + x = -6.119186584

Solving
-3.666666667 + x = -6.119186584

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = -6.119186584 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = -6.119186584 + 3.666666667
x = -6.119186584 + 3.666666667

Combine like terms: -6.119186584 + 3.666666667 = -2.452519917
x = -2.452519917

Simplifying
x = -2.452519917


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.785853251, -2.452519917}

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