3x^2-12x-84=0

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Solution for 3x^2-12x-84=0 equation: 


Simplifying
3x2 + -12x + -84 = 0

Reorder the terms:
-84 + -12x + 3x2 = 0

Solving
-84 + -12x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + -4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-28 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + -4x + x2 = 0

Solving
-28 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -4x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -4x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -4x + x2 = 0 + 28
-4x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-4x + x2 = 28

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 = 28 + 4

Reorder the terms:
4 + -4x + x2 = 28 + 4

Combine like terms: 28 + 4 = 32
4 + -4x + x2 = 32

Factor a perfect square on the left side:
(x + -2)(x + -2) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + -2) equal to 5.656854249 and -5.656854249.


Subproblem 1
x + -2 = 5.656854249

Simplifying
x + -2 = 5.656854249

Reorder the terms:
-2 + x = 5.656854249

Solving
-2 + x = 5.656854249

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 = 5.656854249 + 2

Combine like terms: -2 + 2 = 0
0 + x = 5.656854249 + 2
x = 5.656854249 + 2

Combine like terms: 5.656854249 + 2 = 7.656854249
x = 7.656854249

Simplifying
x = 7.656854249


Subproblem 2
x + -2 = -5.656854249

Simplifying
x + -2 = -5.656854249

Reorder the terms:
-2 + x = -5.656854249

Solving
-2 + x = -5.656854249

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 = -5.656854249 + 2

Combine like terms: -2 + 2 = 0
0 + x = -5.656854249 + 2
x = -5.656854249 + 2

Combine like terms: -5.656854249 + 2 = -3.656854249
x = -3.656854249

Simplifying
x = -3.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.656854249, -3.656854249}
Solution
x = {7.656854249, -3.656854249}

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