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Simplifying -8w = w2 + -15 Reorder the terms: -8w = -15 + w2 Solving -8w = -15 + w2 Solving for variable 'w'. Reorder the terms: 15 + -8w + -1w2 = -15 + w2 + 15 + -1w2 Reorder the terms: 15 + -8w + -1w2 = -15 + 15 + w2 + -1w2 Combine like terms: -15 + 15 = 0 15 + -8w + -1w2 = 0 + w2 + -1w2 15 + -8w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 15 + -8w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 8w + w2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 8w + 15 + w2 = 0 + 15 Reorder the terms: -15 + 15 + 8w + w2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 8w + w2 = 0 + 15 8w + w2 = 0 + 15 Combine like terms: 0 + 15 = 15 8w + w2 = 15 The w term is 8w. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w + 16 + w2 = 15 + 16 Reorder the terms: 16 + 8w + w2 = 15 + 16 Combine like terms: 15 + 16 = 31 16 + 8w + w2 = 31 Factor a perfect square on the left side: (w + 4)(w + 4) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (w + 4) equal to 5.567764363 and -5.567764363.Subproblem 1
w + 4 = 5.567764363 Simplifying w + 4 = 5.567764363 Reorder the terms: 4 + w = 5.567764363 Solving 4 + w = 5.567764363 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + w = 5.567764363 + -4 w = 5.567764363 + -4 Combine like terms: 5.567764363 + -4 = 1.567764363 w = 1.567764363 Simplifying w = 1.567764363Subproblem 2
w + 4 = -5.567764363 Simplifying w + 4 = -5.567764363 Reorder the terms: 4 + w = -5.567764363 Solving 4 + w = -5.567764363 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + w = -5.567764363 + -4 w = -5.567764363 + -4 Combine like terms: -5.567764363 + -4 = -9.567764363 w = -9.567764363 Simplifying w = -9.567764363Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.567764363, -9.567764363}
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