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Simplifying (17 + 2w)(13 + 2w) + -1(221) = 396 Multiply (17 + 2w) * (13 + 2w) (17(13 + 2w) + 2w * (13 + 2w)) + -1(221) = 396 ((13 * 17 + 2w * 17) + 2w * (13 + 2w)) + -1(221) = 396 ((221 + 34w) + 2w * (13 + 2w)) + -1(221) = 396 (221 + 34w + (13 * 2w + 2w * 2w)) + -1(221) = 396 (221 + 34w + (26w + 4w2)) + -1(221) = 396 Combine like terms: 34w + 26w = 60w (221 + 60w + 4w2) + -1(221) = 396 Multiply -1 * 221 221 + 60w + 4w2 + -221 = 396 Reorder the terms: 221 + -221 + 60w + 4w2 = 396 Combine like terms: 221 + -221 = 0 0 + 60w + 4w2 = 396 60w + 4w2 = 396 Solving 60w + 4w2 = 396 Solving for variable 'w'. Reorder the terms: -396 + 60w + 4w2 = 396 + -396 Combine like terms: 396 + -396 = 0 -396 + 60w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-99 + 15w + w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-99 + 15w + w2)' equal to zero and attempt to solve: Simplifying -99 + 15w + w2 = 0 Solving -99 + 15w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 15w + 99 + w2 = 0 + 99 Reorder the terms: -99 + 99 + 15w + w2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 15w + w2 = 0 + 99 15w + w2 = 0 + 99 Combine like terms: 0 + 99 = 99 15w + w2 = 99 The w term is 15w. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15w + 56.25 + w2 = 99 + 56.25 Reorder the terms: 56.25 + 15w + w2 = 99 + 56.25 Combine like terms: 99 + 56.25 = 155.25 56.25 + 15w + w2 = 155.25 Factor a perfect square on the left side: (w + 7.5)(w + 7.5) = 155.25 Calculate the square root of the right side: 12.459935794 Break this problem into two subproblems by setting (w + 7.5) equal to 12.459935794 and -12.459935794.Subproblem 1
w + 7.5 = 12.459935794 Simplifying w + 7.5 = 12.459935794 Reorder the terms: 7.5 + w = 12.459935794 Solving 7.5 + w = 12.459935794 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = 12.459935794 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = 12.459935794 + -7.5 w = 12.459935794 + -7.5 Combine like terms: 12.459935794 + -7.5 = 4.959935794 w = 4.959935794 Simplifying w = 4.959935794Subproblem 2
w + 7.5 = -12.459935794 Simplifying w + 7.5 = -12.459935794 Reorder the terms: 7.5 + w = -12.459935794 Solving 7.5 + w = -12.459935794 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = -12.459935794 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = -12.459935794 + -7.5 w = -12.459935794 + -7.5 Combine like terms: -12.459935794 + -7.5 = -19.959935794 w = -19.959935794 Simplifying w = -19.959935794Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.959935794, -19.959935794}Solution
w = {4.959935794, -19.959935794}
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