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Simplifying w2 + -2w + -60 = 0 Reorder the terms: -60 + -2w + w2 = 0 Solving -60 + -2w + 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 + -2w + 60 + w2 = 0 + 60 Reorder the terms: -60 + 60 + -2w + w2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -2w + w2 = 0 + 60 -2w + w2 = 0 + 60 Combine like terms: 0 + 60 = 60 -2w + w2 = 60 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 60 + 1 Reorder the terms: 1 + -2w + w2 = 60 + 1 Combine like terms: 60 + 1 = 61 1 + -2w + w2 = 61 Factor a perfect square on the left side: (w + -1)(w + -1) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (w + -1) equal to 7.810249676 and -7.810249676.Subproblem 1
w + -1 = 7.810249676 Simplifying w + -1 = 7.810249676 Reorder the terms: -1 + w = 7.810249676 Solving -1 + w = 7.810249676 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 7.810249676 + 1 Combine like terms: -1 + 1 = 0 0 + w = 7.810249676 + 1 w = 7.810249676 + 1 Combine like terms: 7.810249676 + 1 = 8.810249676 w = 8.810249676 Simplifying w = 8.810249676Subproblem 2
w + -1 = -7.810249676 Simplifying w + -1 = -7.810249676 Reorder the terms: -1 + w = -7.810249676 Solving -1 + w = -7.810249676 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -7.810249676 + 1 Combine like terms: -1 + 1 = 0 0 + w = -7.810249676 + 1 w = -7.810249676 + 1 Combine like terms: -7.810249676 + 1 = -6.810249676 w = -6.810249676 Simplifying w = -6.810249676Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.810249676, -6.810249676}
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