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Simplifying (3w + 12)(w + 12) = 336 Reorder the terms: (12 + 3w)(w + 12) = 336 Reorder the terms: (12 + 3w)(12 + w) = 336 Multiply (12 + 3w) * (12 + w) (12(12 + w) + 3w * (12 + w)) = 336 ((12 * 12 + w * 12) + 3w * (12 + w)) = 336 ((144 + 12w) + 3w * (12 + w)) = 336 (144 + 12w + (12 * 3w + w * 3w)) = 336 (144 + 12w + (36w + 3w2)) = 336 Combine like terms: 12w + 36w = 48w (144 + 48w + 3w2) = 336 Solving 144 + 48w + 3w2 = 336 Solving for variable 'w'. Reorder the terms: 144 + -336 + 48w + 3w2 = 336 + -336 Combine like terms: 144 + -336 = -192 -192 + 48w + 3w2 = 336 + -336 Combine like terms: 336 + -336 = 0 -192 + 48w + 3w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-64 + 16w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-64 + 16w + w2)' equal to zero and attempt to solve: Simplifying -64 + 16w + w2 = 0 Solving -64 + 16w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 16w + 64 + w2 = 0 + 64 Reorder the terms: -64 + 64 + 16w + w2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 16w + w2 = 0 + 64 16w + w2 = 0 + 64 Combine like terms: 0 + 64 = 64 16w + w2 = 64 The w term is 16w. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16w + 64 + w2 = 64 + 64 Reorder the terms: 64 + 16w + w2 = 64 + 64 Combine like terms: 64 + 64 = 128 64 + 16w + w2 = 128 Factor a perfect square on the left side: (w + 8)(w + 8) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (w + 8) equal to 11.313708499 and -11.313708499.Subproblem 1
w + 8 = 11.313708499 Simplifying w + 8 = 11.313708499 Reorder the terms: 8 + w = 11.313708499 Solving 8 + w = 11.313708499 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = 11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + w = 11.313708499 + -8 w = 11.313708499 + -8 Combine like terms: 11.313708499 + -8 = 3.313708499 w = 3.313708499 Simplifying w = 3.313708499Subproblem 2
w + 8 = -11.313708499 Simplifying w + 8 = -11.313708499 Reorder the terms: 8 + w = -11.313708499 Solving 8 + w = -11.313708499 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = -11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + w = -11.313708499 + -8 w = -11.313708499 + -8 Combine like terms: -11.313708499 + -8 = -19.313708499 w = -19.313708499 Simplifying w = -19.313708499Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.313708499, -19.313708499}Solution
w = {3.313708499, -19.313708499}
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