4w^2-144w+304=0

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Solution for 4w^2-144w+304=0 equation: 


Simplifying
4w2 + -144w + 304 = 0

Reorder the terms:
304 + -144w + 4w2 = 0

Solving
304 + -144w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(76 + -36w + w2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(76 + -36w + w2)' equal to zero and attempt to solve:

Simplifying
76 + -36w + w2 = 0

Solving
76 + -36w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-76' to each side of the equation.
76 + -36w + -76 + w2 = 0 + -76

Reorder the terms:
76 + -76 + -36w + w2 = 0 + -76

Combine like terms: 76 + -76 = 0
0 + -36w + w2 = 0 + -76
-36w + w2 = 0 + -76

Combine like terms: 0 + -76 = -76
-36w + w2 = -76

The w term is -36w.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36w + 324 + w2 = -76 + 324

Reorder the terms:
324 + -36w + w2 = -76 + 324

Combine like terms: -76 + 324 = 248
324 + -36w + w2 = 248

Factor a perfect square on the left side:
(w + -18)(w + -18) = 248

Calculate the square root of the right side: 15.748015748

Break this problem into two subproblems by setting 
(w + -18) equal to 15.748015748 and -15.748015748.


Subproblem 1
w + -18 = 15.748015748

Simplifying
w + -18 = 15.748015748

Reorder the terms:
-18 + w = 15.748015748

Solving
-18 + w = 15.748015748

Solving for variable 'w'.

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

Add '18' to each side of the equation.
-18 + 18 + w = 15.748015748 + 18

Combine like terms: -18 + 18 = 0
0 + w = 15.748015748 + 18
w = 15.748015748 + 18

Combine like terms: 15.748015748 + 18 = 33.748015748
w = 33.748015748

Simplifying
w = 33.748015748


Subproblem 2
w + -18 = -15.748015748

Simplifying
w + -18 = -15.748015748

Reorder the terms:
-18 + w = -15.748015748

Solving
-18 + w = -15.748015748

Solving for variable 'w'.

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

Add '18' to each side of the equation.
-18 + 18 + w = -15.748015748 + 18

Combine like terms: -18 + 18 = 0
0 + w = -15.748015748 + 18
w = -15.748015748 + 18

Combine like terms: -15.748015748 + 18 = 2.251984252
w = 2.251984252

Simplifying
w = 2.251984252


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {33.748015748, 2.251984252}
Solution
w = {33.748015748, 2.251984252}

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