2w^2+14w-24=0

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Solution for 2w^2+14w-24=0 equation: 


Simplifying
2w2 + 14w + -24 = 0

Reorder the terms:
-24 + 14w + 2w2 = 0

Solving
-24 + 14w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 7w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 7w + w2)' equal to zero and attempt to solve:

Simplifying
-12 + 7w + w2 = 0

Solving
-12 + 7w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 7w + 12 + w2 = 0 + 12

Reorder the terms:
-12 + 12 + 7w + w2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 7w + w2 = 0 + 12
7w + w2 = 0 + 12

Combine like terms: 0 + 12 = 12
7w + w2 = 12

The w term is 7w.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7w + 12.25 + w2 = 12 + 12.25

Reorder the terms:
12.25 + 7w + w2 = 12 + 12.25

Combine like terms: 12 + 12.25 = 24.25
12.25 + 7w + w2 = 24.25

Factor a perfect square on the left side:
(w + 3.5)(w + 3.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(w + 3.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
w + 3.5 = 4.924428901

Simplifying
w + 3.5 = 4.924428901

Reorder the terms:
3.5 + w = 4.924428901

Solving
3.5 + w = 4.924428901

Solving for variable 'w'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + w = 4.924428901 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = 4.924428901 + -3.5
w = 4.924428901 + -3.5

Combine like terms: 4.924428901 + -3.5 = 1.424428901
w = 1.424428901

Simplifying
w = 1.424428901


Subproblem 2
w + 3.5 = -4.924428901

Simplifying
w + 3.5 = -4.924428901

Reorder the terms:
3.5 + w = -4.924428901

Solving
3.5 + w = -4.924428901

Solving for variable 'w'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + w = -4.924428901 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = -4.924428901 + -3.5
w = -4.924428901 + -3.5

Combine like terms: -4.924428901 + -3.5 = -8.424428901
w = -8.424428901

Simplifying
w = -8.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.424428901, -8.424428901}
Solution
w = {1.424428901, -8.424428901}

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