44w^2+12w+9=121

Solution for 44w^2+12w+9=121 equation:

Simplifying
44w2 + 12w + 9 = 121

Reorder the terms:
9 + 12w + 44w2 = 121

Solving
9 + 12w + 44w2 = 121

Solving for variable 'w'.

Reorder the terms:
9 + -121 + 12w + 44w2 = 121 + -121

Combine like terms: 9 + -121 = -112
-112 + 12w + 44w2 = 121 + -121

Combine like terms: 121 + -121 = 0
-112 + 12w + 44w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-28 + 3w + 11w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-28 + 3w + 11w2)' equal to zero and attempt to solve:

Simplifying
-28 + 3w + 11w2 = 0

Solving
-28 + 3w + 11w2 = 0

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

Divide each side by '11'.
-2.545454545 + 0.2727272727w + w2 = 0

Move the constant term to the right:

Add '2.545454545' to each side of the equation.
-2.545454545 + 0.2727272727w + 2.545454545 + w2 = 0 + 2.545454545

Reorder the terms:
-2.545454545 + 2.545454545 + 0.2727272727w + w2 = 0 + 2.545454545

Combine like terms: -2.545454545 + 2.545454545 = 0.000000000
0.000000000 + 0.2727272727w + w2 = 0 + 2.545454545
0.2727272727w + w2 = 0 + 2.545454545

Combine like terms: 0 + 2.545454545 = 2.545454545
0.2727272727w + w2 = 2.545454545

The w term is 0.2727272727w.  Take half its coefficient (0.1363636364).
Square it (0.01859504133) and add it to both sides.

Add '0.01859504133' to each side of the equation.
0.2727272727w + 0.01859504133 + w2 = 2.545454545 + 0.01859504133

Reorder the terms:
0.01859504133 + 0.2727272727w + w2 = 2.545454545 + 0.01859504133

Combine like terms: 2.545454545 + 0.01859504133 = 2.56404958633
0.01859504133 + 0.2727272727w + w2 = 2.56404958633

Factor a perfect square on the left side:
(w + 0.1363636364)(w + 0.1363636364) = 2.56404958633

Calculate the square root of the right side: 1.601264996

Break this problem into two subproblems by setting 
(w + 0.1363636364) equal to 1.601264996 and -1.601264996.

Subproblem 1
w + 0.1363636364 = 1.601264996

Simplifying
w + 0.1363636364 = 1.601264996

Reorder the terms:
0.1363636364 + w = 1.601264996

Solving
0.1363636364 + w = 1.601264996

Solving for variable 'w'.

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

Add '-0.1363636364' to each side of the equation.
0.1363636364 + -0.1363636364 + w = 1.601264996 + -0.1363636364

Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000
0.0000000000 + w = 1.601264996 + -0.1363636364
w = 1.601264996 + -0.1363636364

Combine like terms: 1.601264996 + -0.1363636364 = 1.4649013596
w = 1.4649013596

Simplifying
w = 1.4649013596

Subproblem 2
w + 0.1363636364 = -1.601264996

Simplifying
w + 0.1363636364 = -1.601264996

Reorder the terms:
0.1363636364 + w = -1.601264996

Solving
0.1363636364 + w = -1.601264996

Solving for variable 'w'.

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

Add '-0.1363636364' to each side of the equation.
0.1363636364 + -0.1363636364 + w = -1.601264996 + -0.1363636364

Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000
0.0000000000 + w = -1.601264996 + -0.1363636364
w = -1.601264996 + -0.1363636364

Combine like terms: -1.601264996 + -0.1363636364 = -1.7376286324
w = -1.7376286324

Simplifying
w = -1.7376286324

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.4649013596, -1.7376286324}
Solution
w = {1.4649013596, -1.7376286324}