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Simplifying (13 + 2w)(17 + 2w) = 400 Multiply (13 + 2w) * (17 + 2w) (13(17 + 2w) + 2w * (17 + 2w)) = 400 ((17 * 13 + 2w * 13) + 2w * (17 + 2w)) = 400 ((221 + 26w) + 2w * (17 + 2w)) = 400 (221 + 26w + (17 * 2w + 2w * 2w)) = 400 (221 + 26w + (34w + 4w2)) = 400 Combine like terms: 26w + 34w = 60w (221 + 60w + 4w2) = 400 Solving 221 + 60w + 4w2 = 400 Solving for variable 'w'. Reorder the terms: 221 + -400 + 60w + 4w2 = 400 + -400 Combine like terms: 221 + -400 = -179 -179 + 60w + 4w2 = 400 + -400 Combine like terms: 400 + -400 = 0 -179 + 60w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -44.75 + 15w + w2 = 0 Move the constant term to the right: Add '44.75' to each side of the equation. -44.75 + 15w + 44.75 + w2 = 0 + 44.75 Reorder the terms: -44.75 + 44.75 + 15w + w2 = 0 + 44.75 Combine like terms: -44.75 + 44.75 = 0.00 0.00 + 15w + w2 = 0 + 44.75 15w + w2 = 0 + 44.75 Combine like terms: 0 + 44.75 = 44.75 15w + w2 = 44.75 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 = 44.75 + 56.25 Reorder the terms: 56.25 + 15w + w2 = 44.75 + 56.25 Combine like terms: 44.75 + 56.25 = 101 56.25 + 15w + w2 = 101 Factor a perfect square on the left side: (w + 7.5)(w + 7.5) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (w + 7.5) equal to 10.049875621 and -10.049875621.Subproblem 1
w + 7.5 = 10.049875621 Simplifying w + 7.5 = 10.049875621 Reorder the terms: 7.5 + w = 10.049875621 Solving 7.5 + w = 10.049875621 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 = 10.049875621 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = 10.049875621 + -7.5 w = 10.049875621 + -7.5 Combine like terms: 10.049875621 + -7.5 = 2.549875621 w = 2.549875621 Simplifying w = 2.549875621Subproblem 2
w + 7.5 = -10.049875621 Simplifying w + 7.5 = -10.049875621 Reorder the terms: 7.5 + w = -10.049875621 Solving 7.5 + w = -10.049875621 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 = -10.049875621 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = -10.049875621 + -7.5 w = -10.049875621 + -7.5 Combine like terms: -10.049875621 + -7.5 = -17.549875621 w = -17.549875621 Simplifying w = -17.549875621Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.549875621, -17.549875621}
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