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Simplifying w2 + -33w + -216 = 0 Reorder the terms: -216 + -33w + w2 = 0 Solving -216 + -33w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '216' to each side of the equation. -216 + -33w + 216 + w2 = 0 + 216 Reorder the terms: -216 + 216 + -33w + w2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + -33w + w2 = 0 + 216 -33w + w2 = 0 + 216 Combine like terms: 0 + 216 = 216 -33w + w2 = 216 The w term is -33w. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33w + 272.25 + w2 = 216 + 272.25 Reorder the terms: 272.25 + -33w + w2 = 216 + 272.25 Combine like terms: 216 + 272.25 = 488.25 272.25 + -33w + w2 = 488.25 Factor a perfect square on the left side: (w + -16.5)(w + -16.5) = 488.25 Calculate the square root of the right side: 22.096379794 Break this problem into two subproblems by setting (w + -16.5) equal to 22.096379794 and -22.096379794.Subproblem 1
w + -16.5 = 22.096379794 Simplifying w + -16.5 = 22.096379794 Reorder the terms: -16.5 + w = 22.096379794 Solving -16.5 + w = 22.096379794 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + w = 22.096379794 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + w = 22.096379794 + 16.5 w = 22.096379794 + 16.5 Combine like terms: 22.096379794 + 16.5 = 38.596379794 w = 38.596379794 Simplifying w = 38.596379794Subproblem 2
w + -16.5 = -22.096379794 Simplifying w + -16.5 = -22.096379794 Reorder the terms: -16.5 + w = -22.096379794 Solving -16.5 + w = -22.096379794 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + w = -22.096379794 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + w = -22.096379794 + 16.5 w = -22.096379794 + 16.5 Combine like terms: -22.096379794 + 16.5 = -5.596379794 w = -5.596379794 Simplifying w = -5.596379794Solution
The solution to the problem is based on the solutions from the subproblems. w = {38.596379794, -5.596379794}
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