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Simplifying (w + 5)(w + 13) = 72 Reorder the terms: (5 + w)(w + 13) = 72 Reorder the terms: (5 + w)(13 + w) = 72 Multiply (5 + w) * (13 + w) (5(13 + w) + w(13 + w)) = 72 ((13 * 5 + w * 5) + w(13 + w)) = 72 ((65 + 5w) + w(13 + w)) = 72 (65 + 5w + (13 * w + w * w)) = 72 (65 + 5w + (13w + w2)) = 72 Combine like terms: 5w + 13w = 18w (65 + 18w + w2) = 72 Solving 65 + 18w + w2 = 72 Solving for variable 'w'. Reorder the terms: 65 + -72 + 18w + w2 = 72 + -72 Combine like terms: 65 + -72 = -7 -7 + 18w + w2 = 72 + -72 Combine like terms: 72 + -72 = 0 -7 + 18w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 18w + 7 + w2 = 0 + 7 Reorder the terms: -7 + 7 + 18w + w2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 18w + w2 = 0 + 7 18w + w2 = 0 + 7 Combine like terms: 0 + 7 = 7 18w + w2 = 7 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 = 7 + 81 Reorder the terms: 81 + 18w + w2 = 7 + 81 Combine like terms: 7 + 81 = 88 81 + 18w + w2 = 88 Factor a perfect square on the left side: (w + 9)(w + 9) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (w + 9) equal to 9.38083152 and -9.38083152.Subproblem 1
w + 9 = 9.38083152 Simplifying w + 9 = 9.38083152 Reorder the terms: 9 + w = 9.38083152 Solving 9 + w = 9.38083152 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 = 9.38083152 + -9 Combine like terms: 9 + -9 = 0 0 + w = 9.38083152 + -9 w = 9.38083152 + -9 Combine like terms: 9.38083152 + -9 = 0.38083152 w = 0.38083152 Simplifying w = 0.38083152Subproblem 2
w + 9 = -9.38083152 Simplifying w + 9 = -9.38083152 Reorder the terms: 9 + w = -9.38083152 Solving 9 + w = -9.38083152 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 = -9.38083152 + -9 Combine like terms: 9 + -9 = 0 0 + w = -9.38083152 + -9 w = -9.38083152 + -9 Combine like terms: -9.38083152 + -9 = -18.38083152 w = -18.38083152 Simplifying w = -18.38083152Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.38083152, -18.38083152}
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