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Simplifying w2 + -34w + 96 = 0 Reorder the terms: 96 + -34w + w2 = 0 Solving 96 + -34w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + -34w + -96 + w2 = 0 + -96 Reorder the terms: 96 + -96 + -34w + w2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -34w + w2 = 0 + -96 -34w + w2 = 0 + -96 Combine like terms: 0 + -96 = -96 -34w + w2 = -96 The w term is -34w. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34w + 289 + w2 = -96 + 289 Reorder the terms: 289 + -34w + w2 = -96 + 289 Combine like terms: -96 + 289 = 193 289 + -34w + w2 = 193 Factor a perfect square on the left side: (w + -17)(w + -17) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (w + -17) equal to 13.892443989 and -13.892443989.Subproblem 1
w + -17 = 13.892443989 Simplifying w + -17 = 13.892443989 Reorder the terms: -17 + w = 13.892443989 Solving -17 + w = 13.892443989 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + w = 13.892443989 + 17 Combine like terms: -17 + 17 = 0 0 + w = 13.892443989 + 17 w = 13.892443989 + 17 Combine like terms: 13.892443989 + 17 = 30.892443989 w = 30.892443989 Simplifying w = 30.892443989Subproblem 2
w + -17 = -13.892443989 Simplifying w + -17 = -13.892443989 Reorder the terms: -17 + w = -13.892443989 Solving -17 + w = -13.892443989 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + w = -13.892443989 + 17 Combine like terms: -17 + 17 = 0 0 + w = -13.892443989 + 17 w = -13.892443989 + 17 Combine like terms: -13.892443989 + 17 = 3.107556011 w = 3.107556011 Simplifying w = 3.107556011Solution
The solution to the problem is based on the solutions from the subproblems. w = {30.892443989, 3.107556011}
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