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Simplifying 3w2 = -11w + 6 Reorder the terms: 3w2 = 6 + -11w Solving 3w2 = 6 + -11w Solving for variable 'w'. Reorder the terms: -6 + 11w + 3w2 = 6 + -11w + -6 + 11w Reorder the terms: -6 + 11w + 3w2 = 6 + -6 + -11w + 11w Combine like terms: 6 + -6 = 0 -6 + 11w + 3w2 = 0 + -11w + 11w -6 + 11w + 3w2 = -11w + 11w Combine like terms: -11w + 11w = 0 -6 + 11w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 3.666666667w + w2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 3.666666667w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + 3.666666667w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3.666666667w + w2 = 0 + 2 3.666666667w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 3.666666667w + w2 = 2 The w term is 3.666666667w. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667w + 3.361111114 + w2 = 2 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667w + w2 = 2 + 3.361111114 Combine like terms: 2 + 3.361111114 = 5.361111114 3.361111114 + 3.666666667w + w2 = 5.361111114 Factor a perfect square on the left side: (w + 1.833333334)(w + 1.833333334) = 5.361111114 Calculate the square root of the right side: 2.315407332 Break this problem into two subproblems by setting (w + 1.833333334) equal to 2.315407332 and -2.315407332.Subproblem 1
w + 1.833333334 = 2.315407332 Simplifying w + 1.833333334 = 2.315407332 Reorder the terms: 1.833333334 + w = 2.315407332 Solving 1.833333334 + w = 2.315407332 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + w = 2.315407332 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + w = 2.315407332 + -1.833333334 w = 2.315407332 + -1.833333334 Combine like terms: 2.315407332 + -1.833333334 = 0.482073998 w = 0.482073998 Simplifying w = 0.482073998Subproblem 2
w + 1.833333334 = -2.315407332 Simplifying w + 1.833333334 = -2.315407332 Reorder the terms: 1.833333334 + w = -2.315407332 Solving 1.833333334 + w = -2.315407332 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + w = -2.315407332 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + w = -2.315407332 + -1.833333334 w = -2.315407332 + -1.833333334 Combine like terms: -2.315407332 + -1.833333334 = -4.148740666 w = -4.148740666 Simplifying w = -4.148740666Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.482073998, -4.148740666}
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