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Simplifying w(3w + -2) = 60 Reorder the terms: w(-2 + 3w) = 60 (-2 * w + 3w * w) = 60 (-2w + 3w2) = 60 Solving -2w + 3w2 = 60 Solving for variable 'w'. Reorder the terms: -60 + -2w + 3w2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -2w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -20 + -0.6666666667w + w2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -0.6666666667w + 20 + w2 = 0 + 20 Reorder the terms: -20 + 20 + -0.6666666667w + w2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -0.6666666667w + w2 = 0 + 20 -0.6666666667w + w2 = 0 + 20 Combine like terms: 0 + 20 = 20 -0.6666666667w + w2 = 20 The w term is -0.6666666667w. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667w + 0.1111111112 + w2 = 20 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667w + w2 = 20 + 0.1111111112 Combine like terms: 20 + 0.1111111112 = 20.1111111112 0.1111111112 + -0.6666666667w + w2 = 20.1111111112 Factor a perfect square on the left side: (w + -0.3333333334)(w + -0.3333333334) = 20.1111111112 Calculate the square root of the right side: 4.484541349 Break this problem into two subproblems by setting (w + -0.3333333334) equal to 4.484541349 and -4.484541349.Subproblem 1
w + -0.3333333334 = 4.484541349 Simplifying w + -0.3333333334 = 4.484541349 Reorder the terms: -0.3333333334 + w = 4.484541349 Solving -0.3333333334 + w = 4.484541349 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + w = 4.484541349 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + w = 4.484541349 + 0.3333333334 w = 4.484541349 + 0.3333333334 Combine like terms: 4.484541349 + 0.3333333334 = 4.8178746824 w = 4.8178746824 Simplifying w = 4.8178746824Subproblem 2
w + -0.3333333334 = -4.484541349 Simplifying w + -0.3333333334 = -4.484541349 Reorder the terms: -0.3333333334 + w = -4.484541349 Solving -0.3333333334 + w = -4.484541349 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + w = -4.484541349 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + w = -4.484541349 + 0.3333333334 w = -4.484541349 + 0.3333333334 Combine like terms: -4.484541349 + 0.3333333334 = -4.1512080156 w = -4.1512080156 Simplifying w = -4.1512080156Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.8178746824, -4.1512080156}
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