6x^2+84x-288=0

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Solution for 6x^2+84x-288=0 equation: 


Simplifying
6x2 + 84x + -288 = 0

Reorder the terms:
-288 + 84x + 6x2 = 0

Solving
-288 + 84x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-48 + 14x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-48 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
-48 + 14x + x2 = 0

Solving
-48 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 14x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 14x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 14x + x2 = 0 + 48
14x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
14x + x2 = 48

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 48 + 49

Reorder the terms:
49 + 14x + x2 = 48 + 49

Combine like terms: 48 + 49 = 97
49 + 14x + x2 = 97

Factor a perfect square on the left side:
(x + 7)(x + 7) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + 7) equal to 9.848857802 and -9.848857802.


Subproblem 1
x + 7 = 9.848857802

Simplifying
x + 7 = 9.848857802

Reorder the terms:
7 + x = 9.848857802

Solving
7 + x = 9.848857802

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 9.848857802 + -7

Combine like terms: 7 + -7 = 0
0 + x = 9.848857802 + -7
x = 9.848857802 + -7

Combine like terms: 9.848857802 + -7 = 2.848857802
x = 2.848857802

Simplifying
x = 2.848857802


Subproblem 2
x + 7 = -9.848857802

Simplifying
x + 7 = -9.848857802

Reorder the terms:
7 + x = -9.848857802

Solving
7 + x = -9.848857802

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -9.848857802 + -7

Combine like terms: 7 + -7 = 0
0 + x = -9.848857802 + -7
x = -9.848857802 + -7

Combine like terms: -9.848857802 + -7 = -16.848857802
x = -16.848857802

Simplifying
x = -16.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.848857802, -16.848857802}
Solution
x = {2.848857802, -16.848857802}

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