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Simplifying w2 + w + -60 = 0 Reorder the terms: -60 + w + w2 = 0 Solving -60 + w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + w + 60 + w2 = 0 + 60 Reorder the terms: -60 + 60 + w + w2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + w + w2 = 0 + 60 w + w2 = 0 + 60 Combine like terms: 0 + 60 = 60 w + w2 = 60 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w + 0.25 + w2 = 60 + 0.25 Reorder the terms: 0.25 + w + w2 = 60 + 0.25 Combine like terms: 60 + 0.25 = 60.25 0.25 + w + w2 = 60.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (w + 0.5) equal to 7.762087348 and -7.762087348.Subproblem 1
w + 0.5 = 7.762087348 Simplifying w + 0.5 = 7.762087348 Reorder the terms: 0.5 + w = 7.762087348 Solving 0.5 + w = 7.762087348 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 7.762087348 + -0.5 w = 7.762087348 + -0.5 Combine like terms: 7.762087348 + -0.5 = 7.262087348 w = 7.262087348 Simplifying w = 7.262087348Subproblem 2
w + 0.5 = -7.762087348 Simplifying w + 0.5 = -7.762087348 Reorder the terms: 0.5 + w = -7.762087348 Solving 0.5 + w = -7.762087348 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -7.762087348 + -0.5 w = -7.762087348 + -0.5 Combine like terms: -7.762087348 + -0.5 = -8.262087348 w = -8.262087348 Simplifying w = -8.262087348Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.262087348, -8.262087348}
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