4w^2+12w+9=1169

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Solution for 4w^2+12w+9=1169 equation: 


Simplifying
4w2 + 12w + 9 = 1169

Reorder the terms:
9 + 12w + 4w2 = 1169

Solving
9 + 12w + 4w2 = 1169

Solving for variable 'w'.

Reorder the terms:
9 + -1169 + 12w + 4w2 = 1169 + -1169

Combine like terms: 9 + -1169 = -1160
-1160 + 12w + 4w2 = 1169 + -1169

Combine like terms: 1169 + -1169 = 0
-1160 + 12w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-290 + 3w + w2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-290 + 3w + w2)' equal to zero and attempt to solve:

Simplifying
-290 + 3w + w2 = 0

Solving
-290 + 3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '290' to each side of the equation.
-290 + 3w + 290 + w2 = 0 + 290

Reorder the terms:
-290 + 290 + 3w + w2 = 0 + 290

Combine like terms: -290 + 290 = 0
0 + 3w + w2 = 0 + 290
3w + w2 = 0 + 290

Combine like terms: 0 + 290 = 290
3w + w2 = 290

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 = 290 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 290 + 2.25

Combine like terms: 290 + 2.25 = 292.25
2.25 + 3w + w2 = 292.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 292.25

Calculate the square root of the right side: 17.095320997

Break this problem into two subproblems by setting 
(w + 1.5) equal to 17.095320997 and -17.095320997.


Subproblem 1
w + 1.5 = 17.095320997

Simplifying
w + 1.5 = 17.095320997

Reorder the terms:
1.5 + w = 17.095320997

Solving
1.5 + w = 17.095320997

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 = 17.095320997 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 17.095320997 + -1.5
w = 17.095320997 + -1.5

Combine like terms: 17.095320997 + -1.5 = 15.595320997
w = 15.595320997

Simplifying
w = 15.595320997


Subproblem 2
w + 1.5 = -17.095320997

Simplifying
w + 1.5 = -17.095320997

Reorder the terms:
1.5 + w = -17.095320997

Solving
1.5 + w = -17.095320997

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 = -17.095320997 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -17.095320997 + -1.5
w = -17.095320997 + -1.5

Combine like terms: -17.095320997 + -1.5 = -18.595320997
w = -18.595320997

Simplifying
w = -18.595320997


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {15.595320997, -18.595320997}
Solution
w = {15.595320997, -18.595320997}

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