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Simplifying 9w2 = 30w + -2 Reorder the terms: 9w2 = -2 + 30w Solving 9w2 = -2 + 30w Solving for variable 'w'. Reorder the terms: 2 + -30w + 9w2 = -2 + 30w + 2 + -30w Reorder the terms: 2 + -30w + 9w2 = -2 + 2 + 30w + -30w Combine like terms: -2 + 2 = 0 2 + -30w + 9w2 = 0 + 30w + -30w 2 + -30w + 9w2 = 30w + -30w Combine like terms: 30w + -30w = 0 2 + -30w + 9w2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + -3.333333333w + w2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -3.333333333w + -0.2222222222 + w2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -3.333333333w + w2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -3.333333333w + w2 = 0 + -0.2222222222 -3.333333333w + w2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -3.333333333w + w2 = -0.2222222222 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 = -0.2222222222 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333w + w2 = -0.2222222222 + 2.777777779 Combine like terms: -0.2222222222 + 2.777777779 = 2.5555555568 2.777777779 + -3.333333333w + w2 = 2.5555555568 Factor a perfect square on the left side: (w + -1.666666667)(w + -1.666666667) = 2.5555555568 Calculate the square root of the right side: 1.598610508 Break this problem into two subproblems by setting (w + -1.666666667) equal to 1.598610508 and -1.598610508.Subproblem 1
w + -1.666666667 = 1.598610508 Simplifying w + -1.666666667 = 1.598610508 Reorder the terms: -1.666666667 + w = 1.598610508 Solving -1.666666667 + w = 1.598610508 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 = 1.598610508 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + w = 1.598610508 + 1.666666667 w = 1.598610508 + 1.666666667 Combine like terms: 1.598610508 + 1.666666667 = 3.265277175 w = 3.265277175 Simplifying w = 3.265277175Subproblem 2
w + -1.666666667 = -1.598610508 Simplifying w + -1.666666667 = -1.598610508 Reorder the terms: -1.666666667 + w = -1.598610508 Solving -1.666666667 + w = -1.598610508 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 = -1.598610508 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + w = -1.598610508 + 1.666666667 w = -1.598610508 + 1.666666667 Combine like terms: -1.598610508 + 1.666666667 = 0.068056159 w = 0.068056159 Simplifying w = 0.068056159Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.265277175, 0.068056159}
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