9x^2-29x-12=0

Solution for 9x^2-29x-12=0 equation:

Simplifying
9x2 + -29x + -12 = 0

Reorder the terms:
-12 + -29x + 9x2 = 0

Solving
-12 + -29x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-1.333333333 + -3.222222222x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -3.222222222x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -3.222222222x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -3.222222222x + x2 = 0 + 1.333333333
-3.222222222x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-3.222222222x + x2 = 1.333333333

The x term is -3.222222222x.  Take half its coefficient (-1.611111111).
Square it (2.595679012) and add it to both sides.

Add '2.595679012' to each side of the equation.
-3.222222222x + 2.595679012 + x2 = 1.333333333 + 2.595679012

Reorder the terms:
2.595679012 + -3.222222222x + x2 = 1.333333333 + 2.595679012

Combine like terms: 1.333333333 + 2.595679012 = 3.929012345
2.595679012 + -3.222222222x + x2 = 3.929012345

Factor a perfect square on the left side:
(x + -1.611111111)(x + -1.611111111) = 3.929012345

Calculate the square root of the right side: 1.982173641

Break this problem into two subproblems by setting 
(x + -1.611111111) equal to 1.982173641 and -1.982173641.

Subproblem 1
x + -1.611111111 = 1.982173641

Simplifying
x + -1.611111111 = 1.982173641

Reorder the terms:
-1.611111111 + x = 1.982173641

Solving
-1.611111111 + x = 1.982173641

Solving for variable 'x'.

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

Add '1.611111111' to each side of the equation.
-1.611111111 + 1.611111111 + x = 1.982173641 + 1.611111111

Combine like terms: -1.611111111 + 1.611111111 = 0.000000000
0.000000000 + x = 1.982173641 + 1.611111111
x = 1.982173641 + 1.611111111

Combine like terms: 1.982173641 + 1.611111111 = 3.593284752
x = 3.593284752

Simplifying
x = 3.593284752

Subproblem 2
x + -1.611111111 = -1.982173641

Simplifying
x + -1.611111111 = -1.982173641

Reorder the terms:
-1.611111111 + x = -1.982173641

Solving
-1.611111111 + x = -1.982173641

Solving for variable 'x'.

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

Add '1.611111111' to each side of the equation.
-1.611111111 + 1.611111111 + x = -1.982173641 + 1.611111111

Combine like terms: -1.611111111 + 1.611111111 = 0.000000000
0.000000000 + x = -1.982173641 + 1.611111111
x = -1.982173641 + 1.611111111

Combine like terms: -1.982173641 + 1.611111111 = -0.37106253
x = -0.37106253

Simplifying
x = -0.37106253

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.593284752, -0.37106253}