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Simplifying w2 + -17w + 18 = 0 Reorder the terms: 18 + -17w + w2 = 0 Solving 18 + -17w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -17w + -18 + w2 = 0 + -18 Reorder the terms: 18 + -18 + -17w + w2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -17w + w2 = 0 + -18 -17w + w2 = 0 + -18 Combine like terms: 0 + -18 = -18 -17w + w2 = -18 The w term is -17w. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17w + 72.25 + w2 = -18 + 72.25 Reorder the terms: 72.25 + -17w + w2 = -18 + 72.25 Combine like terms: -18 + 72.25 = 54.25 72.25 + -17w + w2 = 54.25 Factor a perfect square on the left side: (w + -8.5)(w + -8.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (w + -8.5) equal to 7.365459931 and -7.365459931.Subproblem 1
w + -8.5 = 7.365459931 Simplifying w + -8.5 = 7.365459931 Reorder the terms: -8.5 + w = 7.365459931 Solving -8.5 + w = 7.365459931 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + w = 7.365459931 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + w = 7.365459931 + 8.5 w = 7.365459931 + 8.5 Combine like terms: 7.365459931 + 8.5 = 15.865459931 w = 15.865459931 Simplifying w = 15.865459931Subproblem 2
w + -8.5 = -7.365459931 Simplifying w + -8.5 = -7.365459931 Reorder the terms: -8.5 + w = -7.365459931 Solving -8.5 + w = -7.365459931 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + w = -7.365459931 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + w = -7.365459931 + 8.5 w = -7.365459931 + 8.5 Combine like terms: -7.365459931 + 8.5 = 1.134540069 w = 1.134540069 Simplifying w = 1.134540069Solution
The solution to the problem is based on the solutions from the subproblems. w = {15.865459931, 1.134540069}
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