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Simplifying 2W2 + -5W + -85.9 = 0 Reorder the terms: -85.9 + -5W + 2W2 = 0 Solving -85.9 + -5W + 2W2 = 0 Solving for variable 'W'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -42.95 + -2.5W + W2 = 0 Move the constant term to the right: Add '42.95' to each side of the equation. -42.95 + -2.5W + 42.95 + W2 = 0 + 42.95 Reorder the terms: -42.95 + 42.95 + -2.5W + W2 = 0 + 42.95 Combine like terms: -42.95 + 42.95 = 0.00 0.00 + -2.5W + W2 = 0 + 42.95 -2.5W + W2 = 0 + 42.95 Combine like terms: 0 + 42.95 = 42.95 -2.5W + W2 = 42.95 The W term is -2.5W. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5W + 1.5625 + W2 = 42.95 + 1.5625 Reorder the terms: 1.5625 + -2.5W + W2 = 42.95 + 1.5625 Combine like terms: 42.95 + 1.5625 = 44.5125 1.5625 + -2.5W + W2 = 44.5125 Factor a perfect square on the left side: (W + -1.25)(W + -1.25) = 44.5125 Calculate the square root of the right side: 6.671768881 Break this problem into two subproblems by setting (W + -1.25) equal to 6.671768881 and -6.671768881.Subproblem 1
W + -1.25 = 6.671768881 Simplifying W + -1.25 = 6.671768881 Reorder the terms: -1.25 + W = 6.671768881 Solving -1.25 + W = 6.671768881 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + W = 6.671768881 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + W = 6.671768881 + 1.25 W = 6.671768881 + 1.25 Combine like terms: 6.671768881 + 1.25 = 7.921768881 W = 7.921768881 Simplifying W = 7.921768881Subproblem 2
W + -1.25 = -6.671768881 Simplifying W + -1.25 = -6.671768881 Reorder the terms: -1.25 + W = -6.671768881 Solving -1.25 + W = -6.671768881 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + W = -6.671768881 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + W = -6.671768881 + 1.25 W = -6.671768881 + 1.25 Combine like terms: -6.671768881 + 1.25 = -5.421768881 W = -5.421768881 Simplifying W = -5.421768881Solution
The solution to the problem is based on the solutions from the subproblems. W = {7.921768881, -5.421768881}
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