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Simplifying -6w2 + -1w + 11 = 0 Reorder the terms: 11 + -1w + -6w2 = 0 Solving 11 + -1w + -6w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.833333333 + 0.1666666667w + w2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + 0.1666666667w + 1.833333333 + w2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + 0.1666666667w + w2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + 0.1666666667w + w2 = 0 + 1.833333333 0.1666666667w + w2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 0.1666666667w + w2 = 1.833333333 The w term is 0.1666666667w. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667w + 0.006944444447 + w2 = 1.833333333 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667w + w2 = 1.833333333 + 0.006944444447 Combine like terms: 1.833333333 + 0.006944444447 = 1.840277777447 0.006944444447 + 0.1666666667w + w2 = 1.840277777447 Factor a perfect square on the left side: (w + 0.08333333335)(w + 0.08333333335) = 1.840277777447 Calculate the square root of the right side: 1.356568383 Break this problem into two subproblems by setting (w + 0.08333333335) equal to 1.356568383 and -1.356568383.Subproblem 1
w + 0.08333333335 = 1.356568383 Simplifying w + 0.08333333335 = 1.356568383 Reorder the terms: 0.08333333335 + w = 1.356568383 Solving 0.08333333335 + w = 1.356568383 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + w = 1.356568383 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + w = 1.356568383 + -0.08333333335 w = 1.356568383 + -0.08333333335 Combine like terms: 1.356568383 + -0.08333333335 = 1.27323504965 w = 1.27323504965 Simplifying w = 1.27323504965Subproblem 2
w + 0.08333333335 = -1.356568383 Simplifying w + 0.08333333335 = -1.356568383 Reorder the terms: 0.08333333335 + w = -1.356568383 Solving 0.08333333335 + w = -1.356568383 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + w = -1.356568383 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + w = -1.356568383 + -0.08333333335 w = -1.356568383 + -0.08333333335 Combine like terms: -1.356568383 + -0.08333333335 = -1.43990171635 w = -1.43990171635 Simplifying w = -1.43990171635Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.27323504965, -1.43990171635}
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