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Simplifying w(w + 2) = 85 Reorder the terms: w(2 + w) = 85 (2 * w + w * w) = 85 (2w + w2) = 85 Solving 2w + w2 = 85 Solving for variable 'w'. Reorder the terms: -85 + 2w + w2 = 85 + -85 Combine like terms: 85 + -85 = 0 -85 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + 2w + 85 + w2 = 0 + 85 Reorder the terms: -85 + 85 + 2w + w2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 2w + w2 = 0 + 85 2w + w2 = 0 + 85 Combine like terms: 0 + 85 = 85 2w + w2 = 85 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 = 85 + 1 Reorder the terms: 1 + 2w + w2 = 85 + 1 Combine like terms: 85 + 1 = 86 1 + 2w + w2 = 86 Factor a perfect square on the left side: (w + 1)(w + 1) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (w + 1) equal to 9.273618495 and -9.273618495.Subproblem 1
w + 1 = 9.273618495 Simplifying w + 1 = 9.273618495 Reorder the terms: 1 + w = 9.273618495 Solving 1 + w = 9.273618495 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 = 9.273618495 + -1 Combine like terms: 1 + -1 = 0 0 + w = 9.273618495 + -1 w = 9.273618495 + -1 Combine like terms: 9.273618495 + -1 = 8.273618495 w = 8.273618495 Simplifying w = 8.273618495Subproblem 2
w + 1 = -9.273618495 Simplifying w + 1 = -9.273618495 Reorder the terms: 1 + w = -9.273618495 Solving 1 + w = -9.273618495 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 = -9.273618495 + -1 Combine like terms: 1 + -1 = 0 0 + w = -9.273618495 + -1 w = -9.273618495 + -1 Combine like terms: -9.273618495 + -1 = -10.273618495 w = -10.273618495 Simplifying w = -10.273618495Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.273618495, -10.273618495}
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