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Simplifying w2 + -18w + 6 = 0 Reorder the terms: 6 + -18w + w2 = 0 Solving 6 + -18w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -18w + -6 + w2 = 0 + -6 Reorder the terms: 6 + -6 + -18w + w2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -18w + w2 = 0 + -6 -18w + w2 = 0 + -6 Combine like terms: 0 + -6 = -6 -18w + w2 = -6 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 = -6 + 81 Reorder the terms: 81 + -18w + w2 = -6 + 81 Combine like terms: -6 + 81 = 75 81 + -18w + w2 = 75 Factor a perfect square on the left side: (w + -9)(w + -9) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (w + -9) equal to 8.660254038 and -8.660254038.Subproblem 1
w + -9 = 8.660254038 Simplifying w + -9 = 8.660254038 Reorder the terms: -9 + w = 8.660254038 Solving -9 + w = 8.660254038 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 = 8.660254038 + 9 Combine like terms: -9 + 9 = 0 0 + w = 8.660254038 + 9 w = 8.660254038 + 9 Combine like terms: 8.660254038 + 9 = 17.660254038 w = 17.660254038 Simplifying w = 17.660254038Subproblem 2
w + -9 = -8.660254038 Simplifying w + -9 = -8.660254038 Reorder the terms: -9 + w = -8.660254038 Solving -9 + w = -8.660254038 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 = -8.660254038 + 9 Combine like terms: -9 + 9 = 0 0 + w = -8.660254038 + 9 w = -8.660254038 + 9 Combine like terms: -8.660254038 + 9 = 0.339745962 w = 0.339745962 Simplifying w = 0.339745962Solution
The solution to the problem is based on the solutions from the subproblems. w = {17.660254038, 0.339745962}
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