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Simplifying w2 + 19w = 60 Reorder the terms: 19w + w2 = 60 Solving 19w + w2 = 60 Solving for variable 'w'. Reorder the terms: -60 + 19w + w2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 19w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 19w + 60 + w2 = 0 + 60 Reorder the terms: -60 + 60 + 19w + w2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 19w + w2 = 0 + 60 19w + w2 = 0 + 60 Combine like terms: 0 + 60 = 60 19w + w2 = 60 The w term is 19w. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19w + 90.25 + w2 = 60 + 90.25 Reorder the terms: 90.25 + 19w + w2 = 60 + 90.25 Combine like terms: 60 + 90.25 = 150.25 90.25 + 19w + w2 = 150.25 Factor a perfect square on the left side: (w + 9.5)(w + 9.5) = 150.25 Calculate the square root of the right side: 12.257650672 Break this problem into two subproblems by setting (w + 9.5) equal to 12.257650672 and -12.257650672.Subproblem 1
w + 9.5 = 12.257650672 Simplifying w + 9.5 = 12.257650672 Reorder the terms: 9.5 + w = 12.257650672 Solving 9.5 + w = 12.257650672 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + w = 12.257650672 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + w = 12.257650672 + -9.5 w = 12.257650672 + -9.5 Combine like terms: 12.257650672 + -9.5 = 2.757650672 w = 2.757650672 Simplifying w = 2.757650672Subproblem 2
w + 9.5 = -12.257650672 Simplifying w + 9.5 = -12.257650672 Reorder the terms: 9.5 + w = -12.257650672 Solving 9.5 + w = -12.257650672 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + w = -12.257650672 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + w = -12.257650672 + -9.5 w = -12.257650672 + -9.5 Combine like terms: -12.257650672 + -9.5 = -21.757650672 w = -21.757650672 Simplifying w = -21.757650672Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.757650672, -21.757650672}
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