w^2-9w-21=

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Solution for w^2-9w-21= 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 = 10.922616289 w = 10.922616289 Simplifying w = 10.922616289

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 = -1.922616289 w = -1.922616289 Simplifying w = -1.922616289

Solution

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

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