12x^2+19x-8=0

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Solution for 12x^2+19x-8=0 equation: 


Simplifying
12x2 + 19x + -8 = 0

Reorder the terms:
-8 + 19x + 12x2 = 0

Solving
-8 + 19x + 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'.
-0.6666666667 + 1.583333333x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 1.583333333x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 1.583333333x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 1.583333333x + x2 = 0 + 0.6666666667
1.583333333x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
1.583333333x + x2 = 0.6666666667

The x term is 1.583333333x.  Take half its coefficient (0.7916666665).
Square it (0.6267361108) and add it to both sides.

Add '0.6267361108' to each side of the equation.
1.583333333x + 0.6267361108 + x2 = 0.6666666667 + 0.6267361108

Reorder the terms:
0.6267361108 + 1.583333333x + x2 = 0.6666666667 + 0.6267361108

Combine like terms: 0.6666666667 + 0.6267361108 = 1.2934027775
0.6267361108 + 1.583333333x + x2 = 1.2934027775

Factor a perfect square on the left side:
(x + 0.7916666665)(x + 0.7916666665) = 1.2934027775

Calculate the square root of the right side: 1.137278672

Break this problem into two subproblems by setting 
(x + 0.7916666665) equal to 1.137278672 and -1.137278672.


Subproblem 1
x + 0.7916666665 = 1.137278672

Simplifying
x + 0.7916666665 = 1.137278672

Reorder the terms:
0.7916666665 + x = 1.137278672

Solving
0.7916666665 + x = 1.137278672

Solving for variable 'x'.

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

Add '-0.7916666665' to each side of the equation.
0.7916666665 + -0.7916666665 + x = 1.137278672 + -0.7916666665

Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000
0.0000000000 + x = 1.137278672 + -0.7916666665
x = 1.137278672 + -0.7916666665

Combine like terms: 1.137278672 + -0.7916666665 = 0.3456120055
x = 0.3456120055

Simplifying
x = 0.3456120055


Subproblem 2
x + 0.7916666665 = -1.137278672

Simplifying
x + 0.7916666665 = -1.137278672

Reorder the terms:
0.7916666665 + x = -1.137278672

Solving
0.7916666665 + x = -1.137278672

Solving for variable 'x'.

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

Add '-0.7916666665' to each side of the equation.
0.7916666665 + -0.7916666665 + x = -1.137278672 + -0.7916666665

Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000
0.0000000000 + x = -1.137278672 + -0.7916666665
x = -1.137278672 + -0.7916666665

Combine like terms: -1.137278672 + -0.7916666665 = -1.9289453385
x = -1.9289453385

Simplifying
x = -1.9289453385


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3456120055, -1.9289453385}

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