12x^2-3x-28=0

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Solution for 12x^2-3x-28=0 equation: 


Simplifying
12x2 + -3x + -28 = 0

Reorder the terms:
-28 + -3x + 12x2 = 0

Solving
-28 + -3x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-2.333333333 + -0.25x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -0.25x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -0.25x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -0.25x + x2 = 0 + 2.333333333
-0.25x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-0.25x + x2 = 2.333333333

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 = 2.333333333 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 2.333333333 + 0.015625

Combine like terms: 2.333333333 + 0.015625 = 2.348958333
0.015625 + -0.25x + x2 = 2.348958333

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 2.348958333

Calculate the square root of the right side: 1.53263118

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.53263118 and -1.53263118.


Subproblem 1
x + -0.125 = 1.53263118

Simplifying
x + -0.125 = 1.53263118

Reorder the terms:
-0.125 + x = 1.53263118

Solving
-0.125 + x = 1.53263118

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 = 1.53263118 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 1.53263118 + 0.125
x = 1.53263118 + 0.125

Combine like terms: 1.53263118 + 0.125 = 1.65763118
x = 1.65763118

Simplifying
x = 1.65763118


Subproblem 2
x + -0.125 = -1.53263118

Simplifying
x + -0.125 = -1.53263118

Reorder the terms:
-0.125 + x = -1.53263118

Solving
-0.125 + x = -1.53263118

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 = -1.53263118 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -1.53263118 + 0.125
x = -1.53263118 + 0.125

Combine like terms: -1.53263118 + 0.125 = -1.40763118
x = -1.40763118

Simplifying
x = -1.40763118


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.65763118, -1.40763118}

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