2w^2+4w-1152=0

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Solution for 2w^2+4w-1152=0 equation: 


Simplifying
2w2 + 4w + -1152 = 0

Reorder the terms:
-1152 + 4w + 2w2 = 0

Solving
-1152 + 4w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-576 + 2w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-576 + 2w + w2)' equal to zero and attempt to solve:

Simplifying
-576 + 2w + w2 = 0

Solving
-576 + 2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '576' to each side of the equation.
-576 + 2w + 576 + w2 = 0 + 576

Reorder the terms:
-576 + 576 + 2w + w2 = 0 + 576

Combine like terms: -576 + 576 = 0
0 + 2w + w2 = 0 + 576
2w + w2 = 0 + 576

Combine like terms: 0 + 576 = 576
2w + w2 = 576

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 576 + 1

Reorder the terms:
1 + 2w + w2 = 576 + 1

Combine like terms: 576 + 1 = 577
1 + 2w + w2 = 577

Factor a perfect square on the left side:
(w + 1)(w + 1) = 577

Calculate the square root of the right side: 24.020824299

Break this problem into two subproblems by setting 
(w + 1) equal to 24.020824299 and -24.020824299.


Subproblem 1
w + 1 = 24.020824299

Simplifying
w + 1 = 24.020824299

Reorder the terms:
1 + w = 24.020824299

Solving
1 + w = 24.020824299

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = 24.020824299 + -1

Combine like terms: 1 + -1 = 0
0 + w = 24.020824299 + -1
w = 24.020824299 + -1

Combine like terms: 24.020824299 + -1 = 23.020824299
w = 23.020824299

Simplifying
w = 23.020824299


Subproblem 2
w + 1 = -24.020824299

Simplifying
w + 1 = -24.020824299

Reorder the terms:
1 + w = -24.020824299

Solving
1 + w = -24.020824299

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = -24.020824299 + -1

Combine like terms: 1 + -1 = 0
0 + w = -24.020824299 + -1
w = -24.020824299 + -1

Combine like terms: -24.020824299 + -1 = -25.020824299
w = -25.020824299

Simplifying
w = -25.020824299


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {23.020824299, -25.020824299}
Solution
w = {23.020824299, -25.020824299}

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