w^2+7w-24=0

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Solution for w^2+7w-24=0 equation: 


Simplifying
w2 + 7w + -24 = 0

Reorder the terms:
-24 + 7w + w2 = 0

Solving
-24 + 7w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 7w + 24 + w2 = 0 + 24

Reorder the terms:
-24 + 24 + 7w + w2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 7w + w2 = 0 + 24
7w + w2 = 0 + 24

Combine like terms: 0 + 24 = 24
7w + w2 = 24

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 = 24 + 12.25

Reorder the terms:
12.25 + 7w + w2 = 24 + 12.25

Combine like terms: 24 + 12.25 = 36.25
12.25 + 7w + w2 = 36.25

Factor a perfect square on the left side:
(w + 3.5)(w + 3.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(w + 3.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
w + 3.5 = 6.020797289

Simplifying
w + 3.5 = 6.020797289

Reorder the terms:
3.5 + w = 6.020797289

Solving
3.5 + w = 6.020797289

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 = 6.020797289 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = 6.020797289 + -3.5
w = 6.020797289 + -3.5

Combine like terms: 6.020797289 + -3.5 = 2.520797289
w = 2.520797289

Simplifying
w = 2.520797289


Subproblem 2
w + 3.5 = -6.020797289

Simplifying
w + 3.5 = -6.020797289

Reorder the terms:
3.5 + w = -6.020797289

Solving
3.5 + w = -6.020797289

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 = -6.020797289 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = -6.020797289 + -3.5
w = -6.020797289 + -3.5

Combine like terms: -6.020797289 + -3.5 = -9.520797289
w = -9.520797289

Simplifying
w = -9.520797289


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.520797289, -9.520797289}

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