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Simplifying (3w + 3)(3 + w) = 81 Reorder the terms: (3 + 3w)(3 + w) = 81 Multiply (3 + 3w) * (3 + w) (3(3 + w) + 3w * (3 + w)) = 81 ((3 * 3 + w * 3) + 3w * (3 + w)) = 81 ((9 + 3w) + 3w * (3 + w)) = 81 (9 + 3w + (3 * 3w + w * 3w)) = 81 (9 + 3w + (9w + 3w2)) = 81 Combine like terms: 3w + 9w = 12w (9 + 12w + 3w2) = 81 Solving 9 + 12w + 3w2 = 81 Solving for variable 'w'. Reorder the terms: 9 + -81 + 12w + 3w2 = 81 + -81 Combine like terms: 9 + -81 = -72 -72 + 12w + 3w2 = 81 + -81 Combine like terms: 81 + -81 = 0 -72 + 12w + 3w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + 4w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-24 + 4w + w2)' equal to zero and attempt to solve: Simplifying -24 + 4w + w2 = 0 Solving -24 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 4w + 24 + w2 = 0 + 24 Reorder the terms: -24 + 24 + 4w + w2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 4w + w2 = 0 + 24 4w + w2 = 0 + 24 Combine like terms: 0 + 24 = 24 4w + w2 = 24 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 24 + 4 Reorder the terms: 4 + 4w + w2 = 24 + 4 Combine like terms: 24 + 4 = 28 4 + 4w + w2 = 28 Factor a perfect square on the left side: (w + 2)(w + 2) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (w + 2) equal to 5.291502622 and -5.291502622.Subproblem 1
w + 2 = 5.291502622 Simplifying w + 2 = 5.291502622 Reorder the terms: 2 + w = 5.291502622 Solving 2 + w = 5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 5.291502622 + -2 Combine like terms: 2 + -2 = 0 0 + w = 5.291502622 + -2 w = 5.291502622 + -2 Combine like terms: 5.291502622 + -2 = 3.291502622 w = 3.291502622 Simplifying w = 3.291502622Subproblem 2
w + 2 = -5.291502622 Simplifying w + 2 = -5.291502622 Reorder the terms: 2 + w = -5.291502622 Solving 2 + w = -5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -5.291502622 + -2 Combine like terms: 2 + -2 = 0 0 + w = -5.291502622 + -2 w = -5.291502622 + -2 Combine like terms: -5.291502622 + -2 = -7.291502622 w = -7.291502622 Simplifying w = -7.291502622Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.291502622, -7.291502622}Solution
w = {3.291502622, -7.291502622}
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