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Simplifying 2w2 + -10w + 1 = w2 + 16 Reorder the terms: 1 + -10w + 2w2 = w2 + 16 Reorder the terms: 1 + -10w + 2w2 = 16 + w2 Solving 1 + -10w + 2w2 = 16 + w2 Solving for variable 'w'. Reorder the terms: 1 + -16 + -10w + 2w2 + -1w2 = 16 + w2 + -16 + -1w2 Combine like terms: 1 + -16 = -15 -15 + -10w + 2w2 + -1w2 = 16 + w2 + -16 + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 -15 + -10w + 1w2 = 16 + w2 + -16 + -1w2 Reorder the terms: -15 + -10w + 1w2 = 16 + -16 + w2 + -1w2 Combine like terms: 16 + -16 = 0 -15 + -10w + 1w2 = 0 + w2 + -1w2 -15 + -10w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -15 + -10w + 1w2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -10w + 15 + w2 = 0 + 15 Reorder the terms: -15 + 15 + -10w + w2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -10w + w2 = 0 + 15 -10w + w2 = 0 + 15 Combine like terms: 0 + 15 = 15 -10w + w2 = 15 The w term is -10w. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10w + 25 + w2 = 15 + 25 Reorder the terms: 25 + -10w + w2 = 15 + 25 Combine like terms: 15 + 25 = 40 25 + -10w + w2 = 40 Factor a perfect square on the left side: (w + -5)(w + -5) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (w + -5) equal to 6.32455532 and -6.32455532.Subproblem 1
w + -5 = 6.32455532 Simplifying w + -5 = 6.32455532 Reorder the terms: -5 + w = 6.32455532 Solving -5 + w = 6.32455532 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 6.32455532 + 5 Combine like terms: -5 + 5 = 0 0 + w = 6.32455532 + 5 w = 6.32455532 + 5 Combine like terms: 6.32455532 + 5 = 11.32455532 w = 11.32455532 Simplifying w = 11.32455532Subproblem 2
w + -5 = -6.32455532 Simplifying w + -5 = -6.32455532 Reorder the terms: -5 + w = -6.32455532 Solving -5 + w = -6.32455532 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = -6.32455532 + 5 Combine like terms: -5 + 5 = 0 0 + w = -6.32455532 + 5 w = -6.32455532 + 5 Combine like terms: -6.32455532 + 5 = -1.32455532 w = -1.32455532 Simplifying w = -1.32455532Solution
The solution to the problem is based on the solutions from the subproblems. w = {11.32455532, -1.32455532}
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