w^2-18w+9=0

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Solution for w^2-18w+9=0 equation:


Simplifying
w2 + -18w + 9 = 0

Reorder the terms:
9 + -18w + w2 = 0

Solving
9 + -18w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -18w + -9 + w2 = 0 + -9

Reorder the terms:
9 + -9 + -18w + w2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -18w + w2 = 0 + -9
-18w + w2 = 0 + -9

Combine like terms: 0 + -9 = -9
-18w + w2 = -9

The w term is -18w.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18w + 81 + w2 = -9 + 81

Reorder the terms:
81 + -18w + w2 = -9 + 81

Combine like terms: -9 + 81 = 72
81 + -18w + w2 = 72

Factor a perfect square on the left side:
(w + -9)(w + -9) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(w + -9) equal to 8.485281374 and -8.485281374.

Subproblem 1

w + -9 = 8.485281374 Simplifying w + -9 = 8.485281374 Reorder the terms: -9 + w = 8.485281374 Solving -9 + w = 8.485281374 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + w = 8.485281374 + 9 Combine like terms: -9 + 9 = 0 0 + w = 8.485281374 + 9 w = 8.485281374 + 9 Combine like terms: 8.485281374 + 9 = 17.485281374 w = 17.485281374 Simplifying w = 17.485281374

Subproblem 2

w + -9 = -8.485281374 Simplifying w + -9 = -8.485281374 Reorder the terms: -9 + w = -8.485281374 Solving -9 + w = -8.485281374 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + w = -8.485281374 + 9 Combine like terms: -9 + 9 = 0 0 + w = -8.485281374 + 9 w = -8.485281374 + 9 Combine like terms: -8.485281374 + 9 = 0.514718626 w = 0.514718626 Simplifying w = 0.514718626

Solution

The solution to the problem is based on the solutions from the subproblems. w = {17.485281374, 0.514718626}

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