3x^2-12x-68=0

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Solution for 3x^2-12x-68=0 equation: 


Simplifying
3x2 + -12x + -68 = 0

Reorder the terms:
-68 + -12x + 3x2 = 0

Solving
-68 + -12x + 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'.
-22.66666667 + -4x + x2 = 0

Move the constant term to the right:

Add '22.66666667' to each side of the equation.
-22.66666667 + -4x + 22.66666667 + x2 = 0 + 22.66666667

Reorder the terms:
-22.66666667 + 22.66666667 + -4x + x2 = 0 + 22.66666667

Combine like terms: -22.66666667 + 22.66666667 = 0.00000000
0.00000000 + -4x + x2 = 0 + 22.66666667
-4x + x2 = 0 + 22.66666667

Combine like terms: 0 + 22.66666667 = 22.66666667
-4x + x2 = 22.66666667

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 22.66666667 + 4

Reorder the terms:
4 + -4x + x2 = 22.66666667 + 4

Combine like terms: 22.66666667 + 4 = 26.66666667
4 + -4x + x2 = 26.66666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = 26.66666667

Calculate the square root of the right side: 5.163977795

Break this problem into two subproblems by setting 
(x + -2) equal to 5.163977795 and -5.163977795.


Subproblem 1
x + -2 = 5.163977795

Simplifying
x + -2 = 5.163977795

Reorder the terms:
-2 + x = 5.163977795

Solving
-2 + x = 5.163977795

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 5.163977795 + 2

Combine like terms: -2 + 2 = 0
0 + x = 5.163977795 + 2
x = 5.163977795 + 2

Combine like terms: 5.163977795 + 2 = 7.163977795
x = 7.163977795

Simplifying
x = 7.163977795


Subproblem 2
x + -2 = -5.163977795

Simplifying
x + -2 = -5.163977795

Reorder the terms:
-2 + x = -5.163977795

Solving
-2 + x = -5.163977795

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -5.163977795 + 2

Combine like terms: -2 + 2 = 0
0 + x = -5.163977795 + 2
x = -5.163977795 + 2

Combine like terms: -5.163977795 + 2 = -3.163977795
x = -3.163977795

Simplifying
x = -3.163977795


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.163977795, -3.163977795}

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