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Simplifying (3W + -10) * W = 300 Reorder the terms: (-10 + 3W) * W = 300 Reorder the terms for easier multiplication: W(-10 + 3W) = 300 (-10 * W + 3W * W) = 300 (-10W + 3W2) = 300 Solving -10W + 3W2 = 300 Solving for variable 'W'. Reorder the terms: -300 + -10W + 3W2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + -10W + 3W2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -100 + -3.333333333W + W2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -3.333333333W + 100 + W2 = 0 + 100 Reorder the terms: -100 + 100 + -3.333333333W + W2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -3.333333333W + W2 = 0 + 100 -3.333333333W + W2 = 0 + 100 Combine like terms: 0 + 100 = 100 -3.333333333W + W2 = 100 The W term is -3.333333333W. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333W + 2.777777779 + W2 = 100 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333W + W2 = 100 + 2.777777779 Combine like terms: 100 + 2.777777779 = 102.777777779 2.777777779 + -3.333333333W + W2 = 102.777777779 Factor a perfect square on the left side: (W + -1.666666667)(W + -1.666666667) = 102.777777779 Calculate the square root of the right side: 10.137937551 Break this problem into two subproblems by setting (W + -1.666666667) equal to 10.137937551 and -10.137937551.Subproblem 1
W + -1.666666667 = 10.137937551 Simplifying W + -1.666666667 = 10.137937551 Reorder the terms: -1.666666667 + W = 10.137937551 Solving -1.666666667 + W = 10.137937551 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + W = 10.137937551 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + W = 10.137937551 + 1.666666667 W = 10.137937551 + 1.666666667 Combine like terms: 10.137937551 + 1.666666667 = 11.804604218 W = 11.804604218 Simplifying W = 11.804604218Subproblem 2
W + -1.666666667 = -10.137937551 Simplifying W + -1.666666667 = -10.137937551 Reorder the terms: -1.666666667 + W = -10.137937551 Solving -1.666666667 + W = -10.137937551 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + W = -10.137937551 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + W = -10.137937551 + 1.666666667 W = -10.137937551 + 1.666666667 Combine like terms: -10.137937551 + 1.666666667 = -8.471270884 W = -8.471270884 Simplifying W = -8.471270884Solution
The solution to the problem is based on the solutions from the subproblems. W = {11.804604218, -8.471270884}
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