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Simplifying (18 + w)(w) = 560 Reorder the terms for easier multiplication: w(18 + w) = 560 (18 * w + w * w) = 560 (18w + w2) = 560 Solving 18w + w2 = 560 Solving for variable 'w'. Reorder the terms: -560 + 18w + w2 = 560 + -560 Combine like terms: 560 + -560 = 0 -560 + 18w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '560' to each side of the equation. -560 + 18w + 560 + w2 = 0 + 560 Reorder the terms: -560 + 560 + 18w + w2 = 0 + 560 Combine like terms: -560 + 560 = 0 0 + 18w + w2 = 0 + 560 18w + w2 = 0 + 560 Combine like terms: 0 + 560 = 560 18w + w2 = 560 The w term is 18w. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18w + 81 + w2 = 560 + 81 Reorder the terms: 81 + 18w + w2 = 560 + 81 Combine like terms: 560 + 81 = 641 81 + 18w + w2 = 641 Factor a perfect square on the left side: (w + 9)(w + 9) = 641 Calculate the square root of the right side: 25.317977802 Break this problem into two subproblems by setting (w + 9) equal to 25.317977802 and -25.317977802.Subproblem 1
w + 9 = 25.317977802 Simplifying w + 9 = 25.317977802 Reorder the terms: 9 + w = 25.317977802 Solving 9 + w = 25.317977802 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = 25.317977802 + -9 Combine like terms: 9 + -9 = 0 0 + w = 25.317977802 + -9 w = 25.317977802 + -9 Combine like terms: 25.317977802 + -9 = 16.317977802 w = 16.317977802 Simplifying w = 16.317977802Subproblem 2
w + 9 = -25.317977802 Simplifying w + 9 = -25.317977802 Reorder the terms: 9 + w = -25.317977802 Solving 9 + w = -25.317977802 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = -25.317977802 + -9 Combine like terms: 9 + -9 = 0 0 + w = -25.317977802 + -9 w = -25.317977802 + -9 Combine like terms: -25.317977802 + -9 = -34.317977802 w = -34.317977802 Simplifying w = -34.317977802Solution
The solution to the problem is based on the solutions from the subproblems. w = {16.317977802, -34.317977802}
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