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Simplifying (w2) + 13w + 28 = 100 w2 + 13w + 28 = 100 Reorder the terms: 28 + 13w + w2 = 100 Solving 28 + 13w + w2 = 100 Solving for variable 'w'. Reorder the terms: 28 + -100 + 13w + w2 = 100 + -100 Combine like terms: 28 + -100 = -72 -72 + 13w + w2 = 100 + -100 Combine like terms: 100 + -100 = 0 -72 + 13w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 13w + 72 + w2 = 0 + 72 Reorder the terms: -72 + 72 + 13w + w2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 13w + w2 = 0 + 72 13w + w2 = 0 + 72 Combine like terms: 0 + 72 = 72 13w + w2 = 72 The w term is 13w. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13w + 42.25 + w2 = 72 + 42.25 Reorder the terms: 42.25 + 13w + w2 = 72 + 42.25 Combine like terms: 72 + 42.25 = 114.25 42.25 + 13w + w2 = 114.25 Factor a perfect square on the left side: (w + 6.5)(w + 6.5) = 114.25 Calculate the square root of the right side: 10.688779163 Break this problem into two subproblems by setting (w + 6.5) equal to 10.688779163 and -10.688779163.Subproblem 1
w + 6.5 = 10.688779163 Simplifying w + 6.5 = 10.688779163 Reorder the terms: 6.5 + w = 10.688779163 Solving 6.5 + w = 10.688779163 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + w = 10.688779163 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + w = 10.688779163 + -6.5 w = 10.688779163 + -6.5 Combine like terms: 10.688779163 + -6.5 = 4.188779163 w = 4.188779163 Simplifying w = 4.188779163Subproblem 2
w + 6.5 = -10.688779163 Simplifying w + 6.5 = -10.688779163 Reorder the terms: 6.5 + w = -10.688779163 Solving 6.5 + w = -10.688779163 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + w = -10.688779163 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + w = -10.688779163 + -6.5 w = -10.688779163 + -6.5 Combine like terms: -10.688779163 + -6.5 = -17.188779163 w = -17.188779163 Simplifying w = -17.188779163Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.188779163, -17.188779163}
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