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Simplifying w2 + 30w + -15 = 0 Reorder the terms: -15 + 30w + w2 = 0 Solving -15 + 30w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 30w + 15 + w2 = 0 + 15 Reorder the terms: -15 + 15 + 30w + w2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 30w + w2 = 0 + 15 30w + w2 = 0 + 15 Combine like terms: 0 + 15 = 15 30w + w2 = 15 The w term is 30w. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30w + 225 + w2 = 15 + 225 Reorder the terms: 225 + 30w + w2 = 15 + 225 Combine like terms: 15 + 225 = 240 225 + 30w + w2 = 240 Factor a perfect square on the left side: (w + 15)(w + 15) = 240 Calculate the square root of the right side: 15.491933385 Break this problem into two subproblems by setting (w + 15) equal to 15.491933385 and -15.491933385.Subproblem 1
w + 15 = 15.491933385 Simplifying w + 15 = 15.491933385 Reorder the terms: 15 + w = 15.491933385 Solving 15 + w = 15.491933385 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = 15.491933385 + -15 Combine like terms: 15 + -15 = 0 0 + w = 15.491933385 + -15 w = 15.491933385 + -15 Combine like terms: 15.491933385 + -15 = 0.491933385 w = 0.491933385 Simplifying w = 0.491933385Subproblem 2
w + 15 = -15.491933385 Simplifying w + 15 = -15.491933385 Reorder the terms: 15 + w = -15.491933385 Solving 15 + w = -15.491933385 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = -15.491933385 + -15 Combine like terms: 15 + -15 = 0 0 + w = -15.491933385 + -15 w = -15.491933385 + -15 Combine like terms: -15.491933385 + -15 = -30.491933385 w = -30.491933385 Simplifying w = -30.491933385Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.491933385, -30.491933385}
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