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Simplifying w2 + -13w + -46 = 0 Reorder the terms: -46 + -13w + w2 = 0 Solving -46 + -13w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -13w + 46 + w2 = 0 + 46 Reorder the terms: -46 + 46 + -13w + w2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -13w + w2 = 0 + 46 -13w + w2 = 0 + 46 Combine like terms: 0 + 46 = 46 -13w + w2 = 46 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 = 46 + 42.25 Reorder the terms: 42.25 + -13w + w2 = 46 + 42.25 Combine like terms: 46 + 42.25 = 88.25 42.25 + -13w + w2 = 88.25 Factor a perfect square on the left side: (w + -6.5)(w + -6.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (w + -6.5) equal to 9.394147114 and -9.394147114.Subproblem 1
w + -6.5 = 9.394147114 Simplifying w + -6.5 = 9.394147114 Reorder the terms: -6.5 + w = 9.394147114 Solving -6.5 + w = 9.394147114 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 = 9.394147114 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = 9.394147114 + 6.5 w = 9.394147114 + 6.5 Combine like terms: 9.394147114 + 6.5 = 15.894147114 w = 15.894147114 Simplifying w = 15.894147114Subproblem 2
w + -6.5 = -9.394147114 Simplifying w + -6.5 = -9.394147114 Reorder the terms: -6.5 + w = -9.394147114 Solving -6.5 + w = -9.394147114 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 = -9.394147114 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = -9.394147114 + 6.5 w = -9.394147114 + 6.5 Combine like terms: -9.394147114 + 6.5 = -2.894147114 w = -2.894147114 Simplifying w = -2.894147114Solution
The solution to the problem is based on the solutions from the subproblems. w = {15.894147114, -2.894147114}
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