6x^2-24x-72=32

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Solution for 6x^2-24x-72=32 equation: 


Simplifying
6x2 + -24x + -72 = 32

Reorder the terms:
-72 + -24x + 6x2 = 32

Solving
-72 + -24x + 6x2 = 32

Solving for variable 'x'.

Reorder the terms:
-72 + -32 + -24x + 6x2 = 32 + -32

Combine like terms: -72 + -32 = -104
-104 + -24x + 6x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-104 + -24x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-52 + -12x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-52 + -12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-52 + -12x + 3x2 = 0

Solving
-52 + -12x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-17.33333333 + -4x + x2 = 0

Move the constant term to the right:

Add '17.33333333' to each side of the equation.
-17.33333333 + -4x + 17.33333333 + x2 = 0 + 17.33333333

Reorder the terms:
-17.33333333 + 17.33333333 + -4x + x2 = 0 + 17.33333333

Combine like terms: -17.33333333 + 17.33333333 = 0.00000000
0.00000000 + -4x + x2 = 0 + 17.33333333
-4x + x2 = 0 + 17.33333333

Combine like terms: 0 + 17.33333333 = 17.33333333
-4x + x2 = 17.33333333

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 = 17.33333333 + 4

Reorder the terms:
4 + -4x + x2 = 17.33333333 + 4

Combine like terms: 17.33333333 + 4 = 21.33333333
4 + -4x + x2 = 21.33333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 21.33333333

Calculate the square root of the right side: 4.618802153

Break this problem into two subproblems by setting 
(x + -2) equal to 4.618802153 and -4.618802153.


Subproblem 1
x + -2 = 4.618802153

Simplifying
x + -2 = 4.618802153

Reorder the terms:
-2 + x = 4.618802153

Solving
-2 + x = 4.618802153

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 = 4.618802153 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.618802153 + 2
x = 4.618802153 + 2

Combine like terms: 4.618802153 + 2 = 6.618802153
x = 6.618802153

Simplifying
x = 6.618802153


Subproblem 2
x + -2 = -4.618802153

Simplifying
x + -2 = -4.618802153

Reorder the terms:
-2 + x = -4.618802153

Solving
-2 + x = -4.618802153

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 = -4.618802153 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.618802153 + 2
x = -4.618802153 + 2

Combine like terms: -4.618802153 + 2 = -2.618802153
x = -2.618802153

Simplifying
x = -2.618802153


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.618802153, -2.618802153}
Solution
x = {6.618802153, -2.618802153}

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