12x^2-3x-252=0

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Solution for 12x^2-3x-252=0 equation: 


Simplifying
12x2 + -3x + -252 = 0

Reorder the terms:
-252 + -3x + 12x2 = 0

Solving
-252 + -3x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-84 + -1x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-84 + -1x + 4x2)' equal to zero and attempt to solve:

Simplifying
-84 + -1x + 4x2 = 0

Solving
-84 + -1x + 4x2 = 0

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

Divide each side by '4'.
-21 + -0.25x + x2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -0.25x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + -0.25x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -0.25x + x2 = 0 + 21
-0.25x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
-0.25x + x2 = 21

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 21 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 21 + 0.015625

Combine like terms: 21 + 0.015625 = 21.015625
0.015625 + -0.25x + x2 = 21.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 21.015625

Calculate the square root of the right side: 4.584280205

Break this problem into two subproblems by setting 
(x + -0.125) equal to 4.584280205 and -4.584280205.


Subproblem 1
x + -0.125 = 4.584280205

Simplifying
x + -0.125 = 4.584280205

Reorder the terms:
-0.125 + x = 4.584280205

Solving
-0.125 + x = 4.584280205

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 4.584280205 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 4.584280205 + 0.125
x = 4.584280205 + 0.125

Combine like terms: 4.584280205 + 0.125 = 4.709280205
x = 4.709280205

Simplifying
x = 4.709280205


Subproblem 2
x + -0.125 = -4.584280205

Simplifying
x + -0.125 = -4.584280205

Reorder the terms:
-0.125 + x = -4.584280205

Solving
-0.125 + x = -4.584280205

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -4.584280205 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -4.584280205 + 0.125
x = -4.584280205 + 0.125

Combine like terms: -4.584280205 + 0.125 = -4.459280205
x = -4.459280205

Simplifying
x = -4.459280205


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.709280205, -4.459280205}
Solution
x = {4.709280205, -4.459280205}

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