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Simplifying 354 = 3w2 + 5w Reorder the terms: 354 = 5w + 3w2 Solving 354 = 5w + 3w2 Solving for variable 'w'. Reorder the terms: 354 + -5w + -3w2 = 5w + -5w + 3w2 + -3w2 Combine like terms: 5w + -5w = 0 354 + -5w + -3w2 = 0 + 3w2 + -3w2 354 + -5w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 354 + -5w + -3w2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -118 + 1.666666667w + w2 = 0 Move the constant term to the right: Add '118' to each side of the equation. -118 + 1.666666667w + 118 + w2 = 0 + 118 Reorder the terms: -118 + 118 + 1.666666667w + w2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 1.666666667w + w2 = 0 + 118 1.666666667w + w2 = 0 + 118 Combine like terms: 0 + 118 = 118 1.666666667w + w2 = 118 The w term is 1.666666667w. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667w + 0.6944444447 + w2 = 118 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667w + w2 = 118 + 0.6944444447 Combine like terms: 118 + 0.6944444447 = 118.6944444447 0.6944444447 + 1.666666667w + w2 = 118.6944444447 Factor a perfect square on the left side: (w + 0.8333333335)(w + 0.8333333335) = 118.6944444447 Calculate the square root of the right side: 10.894697997 Break this problem into two subproblems by setting (w + 0.8333333335) equal to 10.894697997 and -10.894697997.Subproblem 1
w + 0.8333333335 = 10.894697997 Simplifying w + 0.8333333335 = 10.894697997 Reorder the terms: 0.8333333335 + w = 10.894697997 Solving 0.8333333335 + w = 10.894697997 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + w = 10.894697997 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + w = 10.894697997 + -0.8333333335 w = 10.894697997 + -0.8333333335 Combine like terms: 10.894697997 + -0.8333333335 = 10.0613646635 w = 10.0613646635 Simplifying w = 10.0613646635Subproblem 2
w + 0.8333333335 = -10.894697997 Simplifying w + 0.8333333335 = -10.894697997 Reorder the terms: 0.8333333335 + w = -10.894697997 Solving 0.8333333335 + w = -10.894697997 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + w = -10.894697997 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + w = -10.894697997 + -0.8333333335 w = -10.894697997 + -0.8333333335 Combine like terms: -10.894697997 + -0.8333333335 = -11.7280313305 w = -11.7280313305 Simplifying w = -11.7280313305Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.0613646635, -11.7280313305}
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