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Simplifying (w + 16)(w + 8) = 320 Reorder the terms: (16 + w)(w + 8) = 320 Reorder the terms: (16 + w)(8 + w) = 320 Multiply (16 + w) * (8 + w) (16(8 + w) + w(8 + w)) = 320 ((8 * 16 + w * 16) + w(8 + w)) = 320 ((128 + 16w) + w(8 + w)) = 320 (128 + 16w + (8 * w + w * w)) = 320 (128 + 16w + (8w + w2)) = 320 Combine like terms: 16w + 8w = 24w (128 + 24w + w2) = 320 Solving 128 + 24w + w2 = 320 Solving for variable 'w'. Reorder the terms: 128 + -320 + 24w + w2 = 320 + -320 Combine like terms: 128 + -320 = -192 -192 + 24w + w2 = 320 + -320 Combine like terms: 320 + -320 = 0 -192 + 24w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + 24w + 192 + w2 = 0 + 192 Reorder the terms: -192 + 192 + 24w + w2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 24w + w2 = 0 + 192 24w + w2 = 0 + 192 Combine like terms: 0 + 192 = 192 24w + w2 = 192 The w term is 24w. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24w + 144 + w2 = 192 + 144 Reorder the terms: 144 + 24w + w2 = 192 + 144 Combine like terms: 192 + 144 = 336 144 + 24w + w2 = 336 Factor a perfect square on the left side: (w + 12)(w + 12) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (w + 12) equal to 18.33030278 and -18.33030278.Subproblem 1
w + 12 = 18.33030278 Simplifying w + 12 = 18.33030278 Reorder the terms: 12 + w = 18.33030278 Solving 12 + w = 18.33030278 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + w = 18.33030278 + -12 Combine like terms: 12 + -12 = 0 0 + w = 18.33030278 + -12 w = 18.33030278 + -12 Combine like terms: 18.33030278 + -12 = 6.33030278 w = 6.33030278 Simplifying w = 6.33030278Subproblem 2
w + 12 = -18.33030278 Simplifying w + 12 = -18.33030278 Reorder the terms: 12 + w = -18.33030278 Solving 12 + w = -18.33030278 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + w = -18.33030278 + -12 Combine like terms: 12 + -12 = 0 0 + w = -18.33030278 + -12 w = -18.33030278 + -12 Combine like terms: -18.33030278 + -12 = -30.33030278 w = -30.33030278 Simplifying w = -30.33030278Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.33030278, -30.33030278}
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