12x^2+6x-52=0

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Solution for 12x^2+6x-52=0 equation: 


Simplifying
12x2 + 6x + -52 = 0

Reorder the terms:
-52 + 6x + 12x2 = 0

Solving
-52 + 6x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-26 + 3x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-26 + 3x + 6x2)' equal to zero and attempt to solve:

Simplifying
-26 + 3x + 6x2 = 0

Solving
-26 + 3x + 6x2 = 0

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

Divide each side by '6'.
-4.333333333 + 0.5x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + 0.5x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + 0.5x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + 0.5x + x2 = 0 + 4.333333333
0.5x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
0.5x + x2 = 4.333333333

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 4.333333333 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 4.333333333 + 0.0625

Combine like terms: 4.333333333 + 0.0625 = 4.395833333
0.0625 + 0.5x + x2 = 4.395833333

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 4.395833333

Calculate the square root of the right side: 2.096624271

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.096624271 and -2.096624271.


Subproblem 1
x + 0.25 = 2.096624271

Simplifying
x + 0.25 = 2.096624271

Reorder the terms:
0.25 + x = 2.096624271

Solving
0.25 + x = 2.096624271

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 2.096624271 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 2.096624271 + -0.25
x = 2.096624271 + -0.25

Combine like terms: 2.096624271 + -0.25 = 1.846624271
x = 1.846624271

Simplifying
x = 1.846624271


Subproblem 2
x + 0.25 = -2.096624271

Simplifying
x + 0.25 = -2.096624271

Reorder the terms:
0.25 + x = -2.096624271

Solving
0.25 + x = -2.096624271

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -2.096624271 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -2.096624271 + -0.25
x = -2.096624271 + -0.25

Combine like terms: -2.096624271 + -0.25 = -2.346624271
x = -2.346624271

Simplifying
x = -2.346624271


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.846624271, -2.346624271}
Solution
x = {1.846624271, -2.346624271}

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