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Simplifying 3w2 + -54w = 3 Reorder the terms: -54w + 3w2 = 3 Solving -54w + 3w2 = 3 Solving for variable 'w'. Reorder the terms: -3 + -54w + 3w2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -54w + 3w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -18w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -18w + w2)' equal to zero and attempt to solve: Simplifying -1 + -18w + w2 = 0 Solving -1 + -18w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -18w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -18w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -18w + w2 = 0 + 1 -18w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -18w + w2 = 1 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 = 1 + 81 Reorder the terms: 81 + -18w + w2 = 1 + 81 Combine like terms: 1 + 81 = 82 81 + -18w + w2 = 82 Factor a perfect square on the left side: (w + -9)(w + -9) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (w + -9) equal to 9.055385138 and -9.055385138.Subproblem 1
w + -9 = 9.055385138 Simplifying w + -9 = 9.055385138 Reorder the terms: -9 + w = 9.055385138 Solving -9 + w = 9.055385138 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 = 9.055385138 + 9 Combine like terms: -9 + 9 = 0 0 + w = 9.055385138 + 9 w = 9.055385138 + 9 Combine like terms: 9.055385138 + 9 = 18.055385138 w = 18.055385138 Simplifying w = 18.055385138Subproblem 2
w + -9 = -9.055385138 Simplifying w + -9 = -9.055385138 Reorder the terms: -9 + w = -9.055385138 Solving -9 + w = -9.055385138 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 = -9.055385138 + 9 Combine like terms: -9 + 9 = 0 0 + w = -9.055385138 + 9 w = -9.055385138 + 9 Combine like terms: -9.055385138 + 9 = -0.055385138 w = -0.055385138 Simplifying w = -0.055385138Solution
The solution to the problem is based on the solutions from the subproblems. w = {18.055385138, -0.055385138}Solution
w = {18.055385138, -0.055385138}
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