w^2-9w+2=0

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


Simplifying
w2 + -9w + 2 = 0

Reorder the terms:
2 + -9w + w2 = 0

Solving
2 + -9w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -9w + -2 + w2 = 0 + -2

Reorder the terms:
2 + -2 + -9w + w2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9w + w2 = 0 + -2
-9w + w2 = 0 + -2

Combine like terms: 0 + -2 = -2
-9w + w2 = -2

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 = -2 + 20.25

Reorder the terms:
20.25 + -9w + w2 = -2 + 20.25

Combine like terms: -2 + 20.25 = 18.25
20.25 + -9w + w2 = 18.25

Factor a perfect square on the left side:
(w + -4.5)(w + -4.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(w + -4.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

w + -4.5 = 4.272001873 Simplifying w + -4.5 = 4.272001873 Reorder the terms: -4.5 + w = 4.272001873 Solving -4.5 + w = 4.272001873 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 = 4.272001873 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = 4.272001873 + 4.5 w = 4.272001873 + 4.5 Combine like terms: 4.272001873 + 4.5 = 8.772001873 w = 8.772001873 Simplifying w = 8.772001873

Subproblem 2

w + -4.5 = -4.272001873 Simplifying w + -4.5 = -4.272001873 Reorder the terms: -4.5 + w = -4.272001873 Solving -4.5 + w = -4.272001873 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 = -4.272001873 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = -4.272001873 + 4.5 w = -4.272001873 + 4.5 Combine like terms: -4.272001873 + 4.5 = 0.227998127 w = 0.227998127 Simplifying w = 0.227998127

Solution

The solution to the problem is based on the solutions from the subproblems. w = {8.772001873, 0.227998127}

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