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Simplifying -3w2 + 52w + 18 = 0 Reorder the terms: 18 + 52w + -3w2 = 0 Solving 18 + 52w + -3w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -6 + -17.33333333w + w2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -17.33333333w + 6 + w2 = 0 + 6 Reorder the terms: -6 + 6 + -17.33333333w + w2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -17.33333333w + w2 = 0 + 6 -17.33333333w + w2 = 0 + 6 Combine like terms: 0 + 6 = 6 -17.33333333w + w2 = 6 The w term is -17.33333333w. Take half its coefficient (-8.666666665). Square it (75.11111108) and add it to both sides. Add '75.11111108' to each side of the equation. -17.33333333w + 75.11111108 + w2 = 6 + 75.11111108 Reorder the terms: 75.11111108 + -17.33333333w + w2 = 6 + 75.11111108 Combine like terms: 6 + 75.11111108 = 81.11111108 75.11111108 + -17.33333333w + w2 = 81.11111108 Factor a perfect square on the left side: (w + -8.666666665)(w + -8.666666665) = 81.11111108 Calculate the square root of the right side: 9.006170722 Break this problem into two subproblems by setting (w + -8.666666665) equal to 9.006170722 and -9.006170722.Subproblem 1
w + -8.666666665 = 9.006170722 Simplifying w + -8.666666665 = 9.006170722 Reorder the terms: -8.666666665 + w = 9.006170722 Solving -8.666666665 + w = 9.006170722 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '8.666666665' to each side of the equation. -8.666666665 + 8.666666665 + w = 9.006170722 + 8.666666665 Combine like terms: -8.666666665 + 8.666666665 = 0.000000000 0.000000000 + w = 9.006170722 + 8.666666665 w = 9.006170722 + 8.666666665 Combine like terms: 9.006170722 + 8.666666665 = 17.672837387 w = 17.672837387 Simplifying w = 17.672837387Subproblem 2
w + -8.666666665 = -9.006170722 Simplifying w + -8.666666665 = -9.006170722 Reorder the terms: -8.666666665 + w = -9.006170722 Solving -8.666666665 + w = -9.006170722 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '8.666666665' to each side of the equation. -8.666666665 + 8.666666665 + w = -9.006170722 + 8.666666665 Combine like terms: -8.666666665 + 8.666666665 = 0.000000000 0.000000000 + w = -9.006170722 + 8.666666665 w = -9.006170722 + 8.666666665 Combine like terms: -9.006170722 + 8.666666665 = -0.339504057 w = -0.339504057 Simplifying w = -0.339504057Solution
The solution to the problem is based on the solutions from the subproblems. w = {17.672837387, -0.339504057}
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