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Simplifying 4w2 + 37w + 35 = 0 Reorder the terms: 35 + 37w + 4w2 = 0 Solving 35 + 37w + 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'. 8.75 + 9.25w + w2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + 9.25w + -8.75 + w2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + 9.25w + w2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + 9.25w + w2 = 0 + -8.75 9.25w + w2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 9.25w + w2 = -8.75 The w term is 9.25w. Take half its coefficient (4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. 9.25w + 21.390625 + w2 = -8.75 + 21.390625 Reorder the terms: 21.390625 + 9.25w + w2 = -8.75 + 21.390625 Combine like terms: -8.75 + 21.390625 = 12.640625 21.390625 + 9.25w + w2 = 12.640625 Factor a perfect square on the left side: (w + 4.625)(w + 4.625) = 12.640625 Calculate the square root of the right side: 3.555365663 Break this problem into two subproblems by setting (w + 4.625) equal to 3.555365663 and -3.555365663.Subproblem 1
w + 4.625 = 3.555365663 Simplifying w + 4.625 = 3.555365663 Reorder the terms: 4.625 + w = 3.555365663 Solving 4.625 + w = 3.555365663 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.625' to each side of the equation. 4.625 + -4.625 + w = 3.555365663 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + w = 3.555365663 + -4.625 w = 3.555365663 + -4.625 Combine like terms: 3.555365663 + -4.625 = -1.069634337 w = -1.069634337 Simplifying w = -1.069634337Subproblem 2
w + 4.625 = -3.555365663 Simplifying w + 4.625 = -3.555365663 Reorder the terms: 4.625 + w = -3.555365663 Solving 4.625 + w = -3.555365663 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.625' to each side of the equation. 4.625 + -4.625 + w = -3.555365663 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + w = -3.555365663 + -4.625 w = -3.555365663 + -4.625 Combine like terms: -3.555365663 + -4.625 = -8.180365663 w = -8.180365663 Simplifying w = -8.180365663Solution
The solution to the problem is based on the solutions from the subproblems. w = {-1.069634337, -8.180365663}
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