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Simplifying 4w2 + 29w + -30 = 0 Reorder the terms: -30 + 29w + 4w2 = 0 Solving -30 + 29w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.5 + 7.25w + w2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 7.25w + 7.5 + w2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 7.25w + w2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 7.25w + w2 = 0 + 7.5 7.25w + w2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 7.25w + w2 = 7.5 The w term is 7.25w. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25w + 13.140625 + w2 = 7.5 + 13.140625 Reorder the terms: 13.140625 + 7.25w + w2 = 7.5 + 13.140625 Combine like terms: 7.5 + 13.140625 = 20.640625 13.140625 + 7.25w + w2 = 20.640625 Factor a perfect square on the left side: (w + 3.625)(w + 3.625) = 20.640625 Calculate the square root of the right side: 4.543195461 Break this problem into two subproblems by setting (w + 3.625) equal to 4.543195461 and -4.543195461.Subproblem 1
w + 3.625 = 4.543195461 Simplifying w + 3.625 = 4.543195461 Reorder the terms: 3.625 + w = 4.543195461 Solving 3.625 + w = 4.543195461 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + w = 4.543195461 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + w = 4.543195461 + -3.625 w = 4.543195461 + -3.625 Combine like terms: 4.543195461 + -3.625 = 0.918195461 w = 0.918195461 Simplifying w = 0.918195461Subproblem 2
w + 3.625 = -4.543195461 Simplifying w + 3.625 = -4.543195461 Reorder the terms: 3.625 + w = -4.543195461 Solving 3.625 + w = -4.543195461 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + w = -4.543195461 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + w = -4.543195461 + -3.625 w = -4.543195461 + -3.625 Combine like terms: -4.543195461 + -3.625 = -8.168195461 w = -8.168195461 Simplifying w = -8.168195461Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.918195461, -8.168195461}
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