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Simplifying (3w + -1) * w = 96 Reorder the terms: (-1 + 3w) * w = 96 Reorder the terms for easier multiplication: w(-1 + 3w) = 96 (-1 * w + 3w * w) = 96 (-1w + 3w2) = 96 Solving -1w + 3w2 = 96 Solving for variable 'w'. Reorder the terms: -96 + -1w + 3w2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + -1w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -32 + -0.3333333333w + w2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -0.3333333333w + 32 + w2 = 0 + 32 Reorder the terms: -32 + 32 + -0.3333333333w + w2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -0.3333333333w + w2 = 0 + 32 -0.3333333333w + w2 = 0 + 32 Combine like terms: 0 + 32 = 32 -0.3333333333w + w2 = 32 The w term is -0.3333333333w. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333w + 0.02777777779 + w2 = 32 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333w + w2 = 32 + 0.02777777779 Combine like terms: 32 + 0.02777777779 = 32.02777777779 0.02777777779 + -0.3333333333w + w2 = 32.02777777779 Factor a perfect square on the left side: (w + -0.1666666667)(w + -0.1666666667) = 32.02777777779 Calculate the square root of the right side: 5.659308949 Break this problem into two subproblems by setting (w + -0.1666666667) equal to 5.659308949 and -5.659308949.Subproblem 1
w + -0.1666666667 = 5.659308949 Simplifying w + -0.1666666667 = 5.659308949 Reorder the terms: -0.1666666667 + w = 5.659308949 Solving -0.1666666667 + w = 5.659308949 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + w = 5.659308949 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + w = 5.659308949 + 0.1666666667 w = 5.659308949 + 0.1666666667 Combine like terms: 5.659308949 + 0.1666666667 = 5.8259756157 w = 5.8259756157 Simplifying w = 5.8259756157Subproblem 2
w + -0.1666666667 = -5.659308949 Simplifying w + -0.1666666667 = -5.659308949 Reorder the terms: -0.1666666667 + w = -5.659308949 Solving -0.1666666667 + w = -5.659308949 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + w = -5.659308949 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + w = -5.659308949 + 0.1666666667 w = -5.659308949 + 0.1666666667 Combine like terms: -5.659308949 + 0.1666666667 = -5.4926422823 w = -5.4926422823 Simplifying w = -5.4926422823Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.8259756157, -5.4926422823}
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