=9x^2+29x+16

Solution for =9x^2+29x+16 equation:

Simplifying
0 = 9x2 + 29x + 16

Reorder the terms:
0 = 16 + 29x + 9x2

Solving
0 = 16 + 29x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + -16 = -16
-16 + -29x + -9x2 = 16 + 29x + 9x2 + -16 + -29x + -9x2

Reorder the terms:
-16 + -29x + -9x2 = 16 + -16 + 29x + -29x + 9x2 + -9x2

Combine like terms: 16 + -16 = 0
-16 + -29x + -9x2 = 0 + 29x + -29x + 9x2 + -9x2
-16 + -29x + -9x2 = 29x + -29x + 9x2 + -9x2

Combine like terms: 29x + -29x = 0
-16 + -29x + -9x2 = 0 + 9x2 + -9x2
-16 + -29x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-16 + -29x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 29x + 9x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(16 + 29x + 9x2)' equal to zero and attempt to solve:

Simplifying
16 + 29x + 9x2 = 0

Solving
16 + 29x + 9x2 = 0

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

Divide each side by '9'.
1.777777778 + 3.222222222x + x2 = 0

Move the constant term to the right:

Add '-1.777777778' to each side of the equation.
1.777777778 + 3.222222222x + -1.777777778 + x2 = 0 + -1.777777778

Reorder the terms:
1.777777778 + -1.777777778 + 3.222222222x + x2 = 0 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
0.000000000 + 3.222222222x + x2 = 0 + -1.777777778
3.222222222x + x2 = 0 + -1.777777778

Combine like terms: 0 + -1.777777778 = -1.777777778
3.222222222x + x2 = -1.777777778

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 = -1.777777778 + 2.595679012

Reorder the terms:
2.595679012 + 3.222222222x + x2 = -1.777777778 + 2.595679012

Combine like terms: -1.777777778 + 2.595679012 = 0.817901234
2.595679012 + 3.222222222x + x2 = 0.817901234

Factor a perfect square on the left side:
(x + 1.611111111)(x + 1.611111111) = 0.817901234

Calculate the square root of the right side: 0.904378922

Break this problem into two subproblems by setting 
(x + 1.611111111) equal to 0.904378922 and -0.904378922.

Subproblem 1
x + 1.611111111 = 0.904378922

Simplifying
x + 1.611111111 = 0.904378922

Reorder the terms:
1.611111111 + x = 0.904378922

Solving
1.611111111 + x = 0.904378922

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 = 0.904378922 + -1.611111111

Combine like terms: 1.611111111 + -1.611111111 = 0.000000000
0.000000000 + x = 0.904378922 + -1.611111111
x = 0.904378922 + -1.611111111

Combine like terms: 0.904378922 + -1.611111111 = -0.706732189
x = -0.706732189

Simplifying
x = -0.706732189

Subproblem 2
x + 1.611111111 = -0.904378922

Simplifying
x + 1.611111111 = -0.904378922

Reorder the terms:
1.611111111 + x = -0.904378922

Solving
1.611111111 + x = -0.904378922

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 = -0.904378922 + -1.611111111

Combine like terms: 1.611111111 + -1.611111111 = 0.000000000
0.000000000 + x = -0.904378922 + -1.611111111
x = -0.904378922 + -1.611111111

Combine like terms: -0.904378922 + -1.611111111 = -2.515490033
x = -2.515490033

Simplifying
x = -2.515490033

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.706732189, -2.515490033}
Solution
x = {-0.706732189, -2.515490033}