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Simplifying 2w + w * w = 20 Multiply w * w 2w + w2 = 20 Solving 2w + w2 = 20 Solving for variable 'w'. Reorder the terms: -20 + 2w + w2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 2w + 20 + w2 = 0 + 20 Reorder the terms: -20 + 20 + 2w + w2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 2w + w2 = 0 + 20 2w + w2 = 0 + 20 Combine like terms: 0 + 20 = 20 2w + w2 = 20 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 20 + 1 Reorder the terms: 1 + 2w + w2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + 2w + w2 = 21 Factor a perfect square on the left side: (w + 1)(w + 1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (w + 1) equal to 4.582575695 and -4.582575695.Subproblem 1
w + 1 = 4.582575695 Simplifying w + 1 = 4.582575695 Reorder the terms: 1 + w = 4.582575695 Solving 1 + w = 4.582575695 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + w = 4.582575695 + -1 w = 4.582575695 + -1 Combine like terms: 4.582575695 + -1 = 3.582575695 w = 3.582575695 Simplifying w = 3.582575695Subproblem 2
w + 1 = -4.582575695 Simplifying w + 1 = -4.582575695 Reorder the terms: 1 + w = -4.582575695 Solving 1 + w = -4.582575695 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + w = -4.582575695 + -1 w = -4.582575695 + -1 Combine like terms: -4.582575695 + -1 = -5.582575695 w = -5.582575695 Simplifying w = -5.582575695Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.582575695, -5.582575695}
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