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Simplifying (w + 2)(w + 2) + -2(w + 2) + 9w = 8 Reorder the terms: (2 + w)(w + 2) + -2(w + 2) + 9w = 8 Reorder the terms: (2 + w)(2 + w) + -2(w + 2) + 9w = 8 Multiply (2 + w) * (2 + w) (2(2 + w) + w(2 + w)) + -2(w + 2) + 9w = 8 ((2 * 2 + w * 2) + w(2 + w)) + -2(w + 2) + 9w = 8 ((4 + 2w) + w(2 + w)) + -2(w + 2) + 9w = 8 (4 + 2w + (2 * w + w * w)) + -2(w + 2) + 9w = 8 (4 + 2w + (2w + w2)) + -2(w + 2) + 9w = 8 Combine like terms: 2w + 2w = 4w (4 + 4w + w2) + -2(w + 2) + 9w = 8 Reorder the terms: 4 + 4w + w2 + -2(2 + w) + 9w = 8 4 + 4w + w2 + (2 * -2 + w * -2) + 9w = 8 4 + 4w + w2 + (-4 + -2w) + 9w = 8 Reorder the terms: 4 + -4 + 4w + -2w + 9w + w2 = 8 Combine like terms: 4 + -4 = 0 0 + 4w + -2w + 9w + w2 = 8 4w + -2w + 9w + w2 = 8 Combine like terms: 4w + -2w = 2w 2w + 9w + w2 = 8 Combine like terms: 2w + 9w = 11w 11w + w2 = 8 Solving 11w + w2 = 8 Solving for variable 'w'. Reorder the terms: -8 + 11w + w2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 11w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 11w + 8 + w2 = 0 + 8 Reorder the terms: -8 + 8 + 11w + w2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 11w + w2 = 0 + 8 11w + w2 = 0 + 8 Combine like terms: 0 + 8 = 8 11w + w2 = 8 The w term is 11w. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11w + 30.25 + w2 = 8 + 30.25 Reorder the terms: 30.25 + 11w + w2 = 8 + 30.25 Combine like terms: 8 + 30.25 = 38.25 30.25 + 11w + w2 = 38.25 Factor a perfect square on the left side: (w + 5.5)(w + 5.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (w + 5.5) equal to 6.184658438 and -6.184658438.Subproblem 1
w + 5.5 = 6.184658438 Simplifying w + 5.5 = 6.184658438 Reorder the terms: 5.5 + w = 6.184658438 Solving 5.5 + w = 6.184658438 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + w = 6.184658438 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = 6.184658438 + -5.5 w = 6.184658438 + -5.5 Combine like terms: 6.184658438 + -5.5 = 0.684658438 w = 0.684658438 Simplifying w = 0.684658438Subproblem 2
w + 5.5 = -6.184658438 Simplifying w + 5.5 = -6.184658438 Reorder the terms: 5.5 + w = -6.184658438 Solving 5.5 + w = -6.184658438 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + w = -6.184658438 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = -6.184658438 + -5.5 w = -6.184658438 + -5.5 Combine like terms: -6.184658438 + -5.5 = -11.684658438 w = -11.684658438 Simplifying w = -11.684658438Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.684658438, -11.684658438}
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