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Simplifying (12 + w)(w) = 44 Reorder the terms for easier multiplication: w(12 + w) = 44 (12 * w + w * w) = 44 (12w + w2) = 44 Solving 12w + w2 = 44 Solving for variable 'w'. Reorder the terms: -44 + 12w + w2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 12w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 12w + 44 + w2 = 0 + 44 Reorder the terms: -44 + 44 + 12w + w2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 12w + w2 = 0 + 44 12w + w2 = 0 + 44 Combine like terms: 0 + 44 = 44 12w + w2 = 44 The w term is 12w. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12w + 36 + w2 = 44 + 36 Reorder the terms: 36 + 12w + w2 = 44 + 36 Combine like terms: 44 + 36 = 80 36 + 12w + w2 = 80 Factor a perfect square on the left side: (w + 6)(w + 6) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (w + 6) equal to 8.94427191 and -8.94427191.Subproblem 1
w + 6 = 8.94427191 Simplifying w + 6 = 8.94427191 Reorder the terms: 6 + w = 8.94427191 Solving 6 + w = 8.94427191 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + w = 8.94427191 + -6 Combine like terms: 6 + -6 = 0 0 + w = 8.94427191 + -6 w = 8.94427191 + -6 Combine like terms: 8.94427191 + -6 = 2.94427191 w = 2.94427191 Simplifying w = 2.94427191Subproblem 2
w + 6 = -8.94427191 Simplifying w + 6 = -8.94427191 Reorder the terms: 6 + w = -8.94427191 Solving 6 + w = -8.94427191 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + w = -8.94427191 + -6 Combine like terms: 6 + -6 = 0 0 + w = -8.94427191 + -6 w = -8.94427191 + -6 Combine like terms: -8.94427191 + -6 = -14.94427191 w = -14.94427191 Simplifying w = -14.94427191Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.94427191, -14.94427191}
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