6x^2+12x-81=7

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Solution for 6x^2+12x-81=7 equation: 


Simplifying
6x2 + 12x + -81 = 7

Reorder the terms:
-81 + 12x + 6x2 = 7

Solving
-81 + 12x + 6x2 = 7

Solving for variable 'x'.

Reorder the terms:
-81 + -7 + 12x + 6x2 = 7 + -7

Combine like terms: -81 + -7 = -88
-88 + 12x + 6x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-88 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-44 + 6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-44 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-44 + 6x + 3x2 = 0

Solving
-44 + 6x + 3x2 = 0

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

Divide each side by '3'.
-14.66666667 + 2x + x2 = 0

Move the constant term to the right:

Add '14.66666667' to each side of the equation.
-14.66666667 + 2x + 14.66666667 + x2 = 0 + 14.66666667

Reorder the terms:
-14.66666667 + 14.66666667 + 2x + x2 = 0 + 14.66666667

Combine like terms: -14.66666667 + 14.66666667 = 0.00000000
0.00000000 + 2x + x2 = 0 + 14.66666667
2x + x2 = 0 + 14.66666667

Combine like terms: 0 + 14.66666667 = 14.66666667
2x + x2 = 14.66666667

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 14.66666667 + 1

Reorder the terms:
1 + 2x + x2 = 14.66666667 + 1

Combine like terms: 14.66666667 + 1 = 15.66666667
1 + 2x + x2 = 15.66666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = 15.66666667

Calculate the square root of the right side: 3.958114029

Break this problem into two subproblems by setting 
(x + 1) equal to 3.958114029 and -3.958114029.


Subproblem 1
x + 1 = 3.958114029

Simplifying
x + 1 = 3.958114029

Reorder the terms:
1 + x = 3.958114029

Solving
1 + x = 3.958114029

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.958114029 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.958114029 + -1
x = 3.958114029 + -1

Combine like terms: 3.958114029 + -1 = 2.958114029
x = 2.958114029

Simplifying
x = 2.958114029


Subproblem 2
x + 1 = -3.958114029

Simplifying
x + 1 = -3.958114029

Reorder the terms:
1 + x = -3.958114029

Solving
1 + x = -3.958114029

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.958114029 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.958114029 + -1
x = -3.958114029 + -1

Combine like terms: -3.958114029 + -1 = -4.958114029
x = -4.958114029

Simplifying
x = -4.958114029


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.958114029, -4.958114029}
Solution
x = {2.958114029, -4.958114029}

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