16w^2+48w+36=2

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Solution for 16w^2+48w+36=2 equation: 


Simplifying
16w2 + 48w + 36 = 2

Reorder the terms:
36 + 48w + 16w2 = 2

Solving
36 + 48w + 16w2 = 2

Solving for variable 'w'.

Reorder the terms:
36 + -2 + 48w + 16w2 = 2 + -2

Combine like terms: 36 + -2 = 34
34 + 48w + 16w2 = 2 + -2

Combine like terms: 2 + -2 = 0
34 + 48w + 16w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + 24w + 8w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + 24w + 8w2)' equal to zero and attempt to solve:

Simplifying
17 + 24w + 8w2 = 0

Solving
17 + 24w + 8w2 = 0

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

Divide each side by '8'.
2.125 + 3w + w2 = 0

Move the constant term to the right:

Add '-2.125' to each side of the equation.
2.125 + 3w + -2.125 + w2 = 0 + -2.125

Reorder the terms:
2.125 + -2.125 + 3w + w2 = 0 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + 3w + w2 = 0 + -2.125
3w + w2 = 0 + -2.125

Combine like terms: 0 + -2.125 = -2.125
3w + w2 = -2.125

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = -2.125 + 2.25

Reorder the terms:
2.25 + 3w + w2 = -2.125 + 2.25

Combine like terms: -2.125 + 2.25 = 0.125
2.25 + 3w + w2 = 0.125

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(w + 1.5) equal to 0.353553391 and -0.353553391.


Subproblem 1
w + 1.5 = 0.353553391

Simplifying
w + 1.5 = 0.353553391

Reorder the terms:
1.5 + w = 0.353553391

Solving
1.5 + w = 0.353553391

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 0.353553391 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 0.353553391 + -1.5
w = 0.353553391 + -1.5

Combine like terms: 0.353553391 + -1.5 = -1.146446609
w = -1.146446609

Simplifying
w = -1.146446609


Subproblem 2
w + 1.5 = -0.353553391

Simplifying
w + 1.5 = -0.353553391

Reorder the terms:
1.5 + w = -0.353553391

Solving
1.5 + w = -0.353553391

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -0.353553391 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -0.353553391 + -1.5
w = -0.353553391 + -1.5

Combine like terms: -0.353553391 + -1.5 = -1.853553391
w = -1.853553391

Simplifying
w = -1.853553391


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-1.146446609, -1.853553391}
Solution
w = {-1.146446609, -1.853553391}

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