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Simplifying w(w + 2) = 98 Reorder the terms: w(2 + w) = 98 (2 * w + w * w) = 98 (2w + w2) = 98 Solving 2w + w2 = 98 Solving for variable 'w'. Reorder the terms: -98 + 2w + w2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + 2w + 98 + w2 = 0 + 98 Reorder the terms: -98 + 98 + 2w + w2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 2w + w2 = 0 + 98 2w + w2 = 0 + 98 Combine like terms: 0 + 98 = 98 2w + w2 = 98 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 = 98 + 1 Reorder the terms: 1 + 2w + w2 = 98 + 1 Combine like terms: 98 + 1 = 99 1 + 2w + w2 = 99 Factor a perfect square on the left side: (w + 1)(w + 1) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (w + 1) equal to 9.949874371 and -9.949874371.Subproblem 1
w + 1 = 9.949874371 Simplifying w + 1 = 9.949874371 Reorder the terms: 1 + w = 9.949874371 Solving 1 + w = 9.949874371 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 = 9.949874371 + -1 Combine like terms: 1 + -1 = 0 0 + w = 9.949874371 + -1 w = 9.949874371 + -1 Combine like terms: 9.949874371 + -1 = 8.949874371 w = 8.949874371 Simplifying w = 8.949874371Subproblem 2
w + 1 = -9.949874371 Simplifying w + 1 = -9.949874371 Reorder the terms: 1 + w = -9.949874371 Solving 1 + w = -9.949874371 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 = -9.949874371 + -1 Combine like terms: 1 + -1 = 0 0 + w = -9.949874371 + -1 w = -9.949874371 + -1 Combine like terms: -9.949874371 + -1 = -10.949874371 w = -10.949874371 Simplifying w = -10.949874371Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.949874371, -10.949874371}
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