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Simplifying w2 + -42 + -13w = 0 Reorder the terms: -42 + -13w + w2 = 0 Solving -42 + -13w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -13w + 42 + w2 = 0 + 42 Reorder the terms: -42 + 42 + -13w + w2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -13w + w2 = 0 + 42 -13w + w2 = 0 + 42 Combine like terms: 0 + 42 = 42 -13w + w2 = 42 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 = 42 + 42.25 Reorder the terms: 42.25 + -13w + w2 = 42 + 42.25 Combine like terms: 42 + 42.25 = 84.25 42.25 + -13w + w2 = 84.25 Factor a perfect square on the left side: (w + -6.5)(w + -6.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (w + -6.5) equal to 9.178779875 and -9.178779875.Subproblem 1
w + -6.5 = 9.178779875 Simplifying w + -6.5 = 9.178779875 Reorder the terms: -6.5 + w = 9.178779875 Solving -6.5 + w = 9.178779875 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 = 9.178779875 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = 9.178779875 + 6.5 w = 9.178779875 + 6.5 Combine like terms: 9.178779875 + 6.5 = 15.678779875 w = 15.678779875 Simplifying w = 15.678779875Subproblem 2
w + -6.5 = -9.178779875 Simplifying w + -6.5 = -9.178779875 Reorder the terms: -6.5 + w = -9.178779875 Solving -6.5 + w = -9.178779875 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 = -9.178779875 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = -9.178779875 + 6.5 w = -9.178779875 + 6.5 Combine like terms: -9.178779875 + 6.5 = -2.678779875 w = -2.678779875 Simplifying w = -2.678779875Solution
The solution to the problem is based on the solutions from the subproblems. w = {15.678779875, -2.678779875}
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