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Simplifying (w + 4)(2w + 4) = 196 Reorder the terms: (4 + w)(2w + 4) = 196 Reorder the terms: (4 + w)(4 + 2w) = 196 Multiply (4 + w) * (4 + 2w) (4(4 + 2w) + w(4 + 2w)) = 196 ((4 * 4 + 2w * 4) + w(4 + 2w)) = 196 ((16 + 8w) + w(4 + 2w)) = 196 (16 + 8w + (4 * w + 2w * w)) = 196 (16 + 8w + (4w + 2w2)) = 196 Combine like terms: 8w + 4w = 12w (16 + 12w + 2w2) = 196 Solving 16 + 12w + 2w2 = 196 Solving for variable 'w'. Reorder the terms: 16 + -196 + 12w + 2w2 = 196 + -196 Combine like terms: 16 + -196 = -180 -180 + 12w + 2w2 = 196 + -196 Combine like terms: 196 + -196 = 0 -180 + 12w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 6w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 6w + w2)' equal to zero and attempt to solve: Simplifying -90 + 6w + w2 = 0 Solving -90 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 6w + 90 + w2 = 0 + 90 Reorder the terms: -90 + 90 + 6w + w2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 6w + w2 = 0 + 90 6w + w2 = 0 + 90 Combine like terms: 0 + 90 = 90 6w + w2 = 90 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 90 + 9 Reorder the terms: 9 + 6w + w2 = 90 + 9 Combine like terms: 90 + 9 = 99 9 + 6w + w2 = 99 Factor a perfect square on the left side: (w + 3)(w + 3) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (w + 3) equal to 9.949874371 and -9.949874371.Subproblem 1
w + 3 = 9.949874371 Simplifying w + 3 = 9.949874371 Reorder the terms: 3 + w = 9.949874371 Solving 3 + w = 9.949874371 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 9.949874371 + -3 Combine like terms: 3 + -3 = 0 0 + w = 9.949874371 + -3 w = 9.949874371 + -3 Combine like terms: 9.949874371 + -3 = 6.949874371 w = 6.949874371 Simplifying w = 6.949874371Subproblem 2
w + 3 = -9.949874371 Simplifying w + 3 = -9.949874371 Reorder the terms: 3 + w = -9.949874371 Solving 3 + w = -9.949874371 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -9.949874371 + -3 Combine like terms: 3 + -3 = 0 0 + w = -9.949874371 + -3 w = -9.949874371 + -3 Combine like terms: -9.949874371 + -3 = -12.949874371 w = -12.949874371 Simplifying w = -12.949874371Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.949874371, -12.949874371}Solution
w = {6.949874371, -12.949874371}
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