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Simplifying W2 + 2W + -98 = 0 Reorder the terms: -98 + 2W + W2 = 0 Solving -98 + 2W + W2 = 0 Solving for variable 'W'. 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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