12x^2+18x-82=0

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Solution for 12x^2+18x-82=0 equation: 


Simplifying
12x2 + 18x + -82 = 0

Reorder the terms:
-82 + 18x + 12x2 = 0

Solving
-82 + 18x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + 9x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-41 + 9x + 6x2)' equal to zero and attempt to solve:

Simplifying
-41 + 9x + 6x2 = 0

Solving
-41 + 9x + 6x2 = 0

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

Divide each side by '6'.
-6.833333333 + 1.5x + x2 = 0

Move the constant term to the right:

Add '6.833333333' to each side of the equation.
-6.833333333 + 1.5x + 6.833333333 + x2 = 0 + 6.833333333

Reorder the terms:
-6.833333333 + 6.833333333 + 1.5x + x2 = 0 + 6.833333333

Combine like terms: -6.833333333 + 6.833333333 = 0.000000000
0.000000000 + 1.5x + x2 = 0 + 6.833333333
1.5x + x2 = 0 + 6.833333333

Combine like terms: 0 + 6.833333333 = 6.833333333
1.5x + x2 = 6.833333333

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 6.833333333 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 6.833333333 + 0.5625

Combine like terms: 6.833333333 + 0.5625 = 7.395833333
0.5625 + 1.5x + x2 = 7.395833333

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 7.395833333

Calculate the square root of the right side: 2.719528145

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.719528145 and -2.719528145.


Subproblem 1
x + 0.75 = 2.719528145

Simplifying
x + 0.75 = 2.719528145

Reorder the terms:
0.75 + x = 2.719528145

Solving
0.75 + x = 2.719528145

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 2.719528145 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 2.719528145 + -0.75
x = 2.719528145 + -0.75

Combine like terms: 2.719528145 + -0.75 = 1.969528145
x = 1.969528145

Simplifying
x = 1.969528145


Subproblem 2
x + 0.75 = -2.719528145

Simplifying
x + 0.75 = -2.719528145

Reorder the terms:
0.75 + x = -2.719528145

Solving
0.75 + x = -2.719528145

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -2.719528145 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -2.719528145 + -0.75
x = -2.719528145 + -0.75

Combine like terms: -2.719528145 + -0.75 = -3.469528145
x = -3.469528145

Simplifying
x = -3.469528145


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.969528145, -3.469528145}
Solution
x = {1.969528145, -3.469528145}

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