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Simplifying w2 + 3w = 77 Reorder the terms: 3w + w2 = 77 Solving 3w + w2 = 77 Solving for variable 'w'. Reorder the terms: -77 + 3w + w2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + 3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 3w + 77 + w2 = 0 + 77 Reorder the terms: -77 + 77 + 3w + w2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 3w + w2 = 0 + 77 3w + w2 = 0 + 77 Combine like terms: 0 + 77 = 77 3w + w2 = 77 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 77 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 77 + 2.25 Combine like terms: 77 + 2.25 = 79.25 2.25 + 3w + w2 = 79.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 79.25 Calculate the square root of the right side: 8.902246907 Break this problem into two subproblems by setting (w + 1.5) equal to 8.902246907 and -8.902246907.Subproblem 1
w + 1.5 = 8.902246907 Simplifying w + 1.5 = 8.902246907 Reorder the terms: 1.5 + w = 8.902246907 Solving 1.5 + w = 8.902246907 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 8.902246907 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 8.902246907 + -1.5 w = 8.902246907 + -1.5 Combine like terms: 8.902246907 + -1.5 = 7.402246907 w = 7.402246907 Simplifying w = 7.402246907Subproblem 2
w + 1.5 = -8.902246907 Simplifying w + 1.5 = -8.902246907 Reorder the terms: 1.5 + w = -8.902246907 Solving 1.5 + w = -8.902246907 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -8.902246907 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -8.902246907 + -1.5 w = -8.902246907 + -1.5 Combine like terms: -8.902246907 + -1.5 = -10.402246907 w = -10.402246907 Simplifying w = -10.402246907Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.402246907, -10.402246907}
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