w^2+9w-21=0

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Solution for w^2+9w-21=0 equation: 


Simplifying
w2 + 9w + -21 = 0

Reorder the terms:
-21 + 9w + w2 = 0

Solving
-21 + 9w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 9w + 21 + w2 = 0 + 21

Reorder the terms:
-21 + 21 + 9w + w2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 9w + w2 = 0 + 21
9w + w2 = 0 + 21

Combine like terms: 0 + 21 = 21
9w + w2 = 21

The w term is 9w.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9w + 20.25 + w2 = 21 + 20.25

Reorder the terms:
20.25 + 9w + w2 = 21 + 20.25

Combine like terms: 21 + 20.25 = 41.25
20.25 + 9w + w2 = 41.25

Factor a perfect square on the left side:
(w + 4.5)(w + 4.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(w + 4.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
w + 4.5 = 6.422616289

Simplifying
w + 4.5 = 6.422616289

Reorder the terms:
4.5 + w = 6.422616289

Solving
4.5 + w = 6.422616289

Solving for variable 'w'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w = 6.422616289 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = 6.422616289 + -4.5
w = 6.422616289 + -4.5

Combine like terms: 6.422616289 + -4.5 = 1.922616289
w = 1.922616289

Simplifying
w = 1.922616289


Subproblem 2
w + 4.5 = -6.422616289

Simplifying
w + 4.5 = -6.422616289

Reorder the terms:
4.5 + w = -6.422616289

Solving
4.5 + w = -6.422616289

Solving for variable 'w'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w = -6.422616289 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = -6.422616289 + -4.5
w = -6.422616289 + -4.5

Combine like terms: -6.422616289 + -4.5 = -10.922616289
w = -10.922616289

Simplifying
w = -10.922616289


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.922616289, -10.922616289}

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