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Simplifying 2w2 + 36w = 72 Reorder the terms: 36w + 2w2 = 72 Solving 36w + 2w2 = 72 Solving for variable 'w'. Reorder the terms: -72 + 36w + 2w2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + 36w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + 18w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + 18w + w2)' equal to zero and attempt to solve: Simplifying -36 + 18w + w2 = 0 Solving -36 + 18w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 18w + 36 + w2 = 0 + 36 Reorder the terms: -36 + 36 + 18w + w2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 18w + w2 = 0 + 36 18w + w2 = 0 + 36 Combine like terms: 0 + 36 = 36 18w + w2 = 36 The w term is 18w. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18w + 81 + w2 = 36 + 81 Reorder the terms: 81 + 18w + w2 = 36 + 81 Combine like terms: 36 + 81 = 117 81 + 18w + w2 = 117 Factor a perfect square on the left side: (w + 9)(w + 9) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (w + 9) equal to 10.816653826 and -10.816653826.Subproblem 1
w + 9 = 10.816653826 Simplifying w + 9 = 10.816653826 Reorder the terms: 9 + w = 10.816653826 Solving 9 + w = 10.816653826 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = 10.816653826 + -9 Combine like terms: 9 + -9 = 0 0 + w = 10.816653826 + -9 w = 10.816653826 + -9 Combine like terms: 10.816653826 + -9 = 1.816653826 w = 1.816653826 Simplifying w = 1.816653826Subproblem 2
w + 9 = -10.816653826 Simplifying w + 9 = -10.816653826 Reorder the terms: 9 + w = -10.816653826 Solving 9 + w = -10.816653826 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = -10.816653826 + -9 Combine like terms: 9 + -9 = 0 0 + w = -10.816653826 + -9 w = -10.816653826 + -9 Combine like terms: -10.816653826 + -9 = -19.816653826 w = -19.816653826 Simplifying w = -19.816653826Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.816653826, -19.816653826}Solution
w = {1.816653826, -19.816653826}
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