w^2-9w+7=0

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Solution for w^2-9w+7=0 equation: 


Simplifying
w2 + -9w + 7 = 0

Reorder the terms:
7 + -9w + w2 = 0

Solving
7 + -9w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -9w + -7 + w2 = 0 + -7

Reorder the terms:
7 + -7 + -9w + w2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9w + w2 = 0 + -7
-9w + w2 = 0 + -7

Combine like terms: 0 + -7 = -7
-9w + w2 = -7

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 = -7 + 20.25

Reorder the terms:
20.25 + -9w + w2 = -7 + 20.25

Combine like terms: -7 + 20.25 = 13.25
20.25 + -9w + w2 = 13.25

Factor a perfect square on the left side:
(w + -4.5)(w + -4.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(w + -4.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
w + -4.5 = 3.640054945

Simplifying
w + -4.5 = 3.640054945

Reorder the terms:
-4.5 + w = 3.640054945

Solving
-4.5 + w = 3.640054945

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 = 3.640054945 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + w = 3.640054945 + 4.5
w = 3.640054945 + 4.5

Combine like terms: 3.640054945 + 4.5 = 8.140054945
w = 8.140054945

Simplifying
w = 8.140054945


Subproblem 2
w + -4.5 = -3.640054945

Simplifying
w + -4.5 = -3.640054945

Reorder the terms:
-4.5 + w = -3.640054945

Solving
-4.5 + w = -3.640054945

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 = -3.640054945 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + w = -3.640054945 + 4.5
w = -3.640054945 + 4.5

Combine like terms: -3.640054945 + 4.5 = 0.859945055
w = 0.859945055

Simplifying
w = 0.859945055


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.140054945, 0.859945055}

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