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Simplifying w2 + 7w = 90 Reorder the terms: 7w + w2 = 90 Solving 7w + w2 = 90 Solving for variable 'w'. Reorder the terms: -90 + 7w + w2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 7w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 7w + 90 + w2 = 0 + 90 Reorder the terms: -90 + 90 + 7w + w2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 7w + w2 = 0 + 90 7w + w2 = 0 + 90 Combine like terms: 0 + 90 = 90 7w + w2 = 90 The w term is 7w. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7w + 12.25 + w2 = 90 + 12.25 Reorder the terms: 12.25 + 7w + w2 = 90 + 12.25 Combine like terms: 90 + 12.25 = 102.25 12.25 + 7w + w2 = 102.25 Factor a perfect square on the left side: (w + 3.5)(w + 3.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (w + 3.5) equal to 10.111874208 and -10.111874208.Subproblem 1
w + 3.5 = 10.111874208 Simplifying w + 3.5 = 10.111874208 Reorder the terms: 3.5 + w = 10.111874208 Solving 3.5 + w = 10.111874208 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = 10.111874208 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 10.111874208 + -3.5 w = 10.111874208 + -3.5 Combine like terms: 10.111874208 + -3.5 = 6.611874208 w = 6.611874208 Simplifying w = 6.611874208Subproblem 2
w + 3.5 = -10.111874208 Simplifying w + 3.5 = -10.111874208 Reorder the terms: 3.5 + w = -10.111874208 Solving 3.5 + w = -10.111874208 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = -10.111874208 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -10.111874208 + -3.5 w = -10.111874208 + -3.5 Combine like terms: -10.111874208 + -3.5 = -13.611874208 w = -13.611874208 Simplifying w = -13.611874208Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.611874208, -13.611874208}
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