w^2-66w+200=0

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Solution for w^2-66w+200=0 equation:


Simplifying
w2 + -66w + 200 = 0

Reorder the terms:
200 + -66w + w2 = 0

Solving
200 + -66w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -66w + -200 + w2 = 0 + -200

Reorder the terms:
200 + -200 + -66w + w2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -66w + w2 = 0 + -200
-66w + w2 = 0 + -200

Combine like terms: 0 + -200 = -200
-66w + w2 = -200

The w term is -66w.  Take half its coefficient (-33).
Square it (1089) and add it to both sides.

Add '1089' to each side of the equation.
-66w + 1089 + w2 = -200 + 1089

Reorder the terms:
1089 + -66w + w2 = -200 + 1089

Combine like terms: -200 + 1089 = 889
1089 + -66w + w2 = 889

Factor a perfect square on the left side:
(w + -33)(w + -33) = 889

Calculate the square root of the right side: 29.816103032

Break this problem into two subproblems by setting 
(w + -33) equal to 29.816103032 and -29.816103032.

Subproblem 1

w + -33 = 29.816103032 Simplifying w + -33 = 29.816103032 Reorder the terms: -33 + w = 29.816103032 Solving -33 + w = 29.816103032 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + w = 29.816103032 + 33 Combine like terms: -33 + 33 = 0 0 + w = 29.816103032 + 33 w = 29.816103032 + 33 Combine like terms: 29.816103032 + 33 = 62.816103032 w = 62.816103032 Simplifying w = 62.816103032

Subproblem 2

w + -33 = -29.816103032 Simplifying w + -33 = -29.816103032 Reorder the terms: -33 + w = -29.816103032 Solving -33 + w = -29.816103032 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + w = -29.816103032 + 33 Combine like terms: -33 + 33 = 0 0 + w = -29.816103032 + 33 w = -29.816103032 + 33 Combine like terms: -29.816103032 + 33 = 3.183896968 w = 3.183896968 Simplifying w = 3.183896968

Solution

The solution to the problem is based on the solutions from the subproblems. w = {62.816103032, 3.183896968}

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