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Simplifying (w + 5)(w + -2) = 36100 Reorder the terms: (5 + w)(w + -2) = 36100 Reorder the terms: (5 + w)(-2 + w) = 36100 Multiply (5 + w) * (-2 + w) (5(-2 + w) + w(-2 + w)) = 36100 ((-2 * 5 + w * 5) + w(-2 + w)) = 36100 ((-10 + 5w) + w(-2 + w)) = 36100 (-10 + 5w + (-2 * w + w * w)) = 36100 (-10 + 5w + (-2w + w2)) = 36100 Combine like terms: 5w + -2w = 3w (-10 + 3w + w2) = 36100 Solving -10 + 3w + w2 = 36100 Solving for variable 'w'. Reorder the terms: -10 + -36100 + 3w + w2 = 36100 + -36100 Combine like terms: -10 + -36100 = -36110 -36110 + 3w + w2 = 36100 + -36100 Combine like terms: 36100 + -36100 = 0 -36110 + 3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '36110' to each side of the equation. -36110 + 3w + 36110 + w2 = 0 + 36110 Reorder the terms: -36110 + 36110 + 3w + w2 = 0 + 36110 Combine like terms: -36110 + 36110 = 0 0 + 3w + w2 = 0 + 36110 3w + w2 = 0 + 36110 Combine like terms: 0 + 36110 = 36110 3w + w2 = 36110 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 = 36110 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 36110 + 2.25 Combine like terms: 36110 + 2.25 = 36112.25 2.25 + 3w + w2 = 36112.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 36112.25 Calculate the square root of the right side: 190.032234108 Break this problem into two subproblems by setting (w + 1.5) equal to 190.032234108 and -190.032234108.Subproblem 1
w + 1.5 = 190.032234108 Simplifying w + 1.5 = 190.032234108 Reorder the terms: 1.5 + w = 190.032234108 Solving 1.5 + w = 190.032234108 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 = 190.032234108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 190.032234108 + -1.5 w = 190.032234108 + -1.5 Combine like terms: 190.032234108 + -1.5 = 188.532234108 w = 188.532234108 Simplifying w = 188.532234108Subproblem 2
w + 1.5 = -190.032234108 Simplifying w + 1.5 = -190.032234108 Reorder the terms: 1.5 + w = -190.032234108 Solving 1.5 + w = -190.032234108 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 = -190.032234108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -190.032234108 + -1.5 w = -190.032234108 + -1.5 Combine like terms: -190.032234108 + -1.5 = -191.532234108 w = -191.532234108 Simplifying w = -191.532234108Solution
The solution to the problem is based on the solutions from the subproblems. w = {188.532234108, -191.532234108}
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