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Simplifying 33 + 15w = 3w * w + 4w Multiply w * w 33 + 15w = 3w2 + 4w Reorder the terms: 33 + 15w = 4w + 3w2 Solving 33 + 15w = 4w + 3w2 Solving for variable 'w'. Combine like terms: 15w + -4w = 11w 33 + 11w + -3w2 = 4w + 3w2 + -4w + -3w2 Reorder the terms: 33 + 11w + -3w2 = 4w + -4w + 3w2 + -3w2 Combine like terms: 4w + -4w = 0 33 + 11w + -3w2 = 0 + 3w2 + -3w2 33 + 11w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 33 + 11w + -3w2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -11 + -3.666666667w + w2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -3.666666667w + 11 + w2 = 0 + 11 Reorder the terms: -11 + 11 + -3.666666667w + w2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -3.666666667w + w2 = 0 + 11 -3.666666667w + w2 = 0 + 11 Combine like terms: 0 + 11 = 11 -3.666666667w + w2 = 11 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 = 11 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667w + w2 = 11 + 3.361111114 Combine like terms: 11 + 3.361111114 = 14.361111114 3.361111114 + -3.666666667w + w2 = 14.361111114 Factor a perfect square on the left side: (w + -1.833333334)(w + -1.833333334) = 14.361111114 Calculate the square root of the right side: 3.789605667 Break this problem into two subproblems by setting (w + -1.833333334) equal to 3.789605667 and -3.789605667.Subproblem 1
w + -1.833333334 = 3.789605667 Simplifying w + -1.833333334 = 3.789605667 Reorder the terms: -1.833333334 + w = 3.789605667 Solving -1.833333334 + w = 3.789605667 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 = 3.789605667 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + w = 3.789605667 + 1.833333334 w = 3.789605667 + 1.833333334 Combine like terms: 3.789605667 + 1.833333334 = 5.622939001 w = 5.622939001 Simplifying w = 5.622939001Subproblem 2
w + -1.833333334 = -3.789605667 Simplifying w + -1.833333334 = -3.789605667 Reorder the terms: -1.833333334 + w = -3.789605667 Solving -1.833333334 + w = -3.789605667 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 = -3.789605667 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + w = -3.789605667 + 1.833333334 w = -3.789605667 + 1.833333334 Combine like terms: -3.789605667 + 1.833333334 = -1.956272333 w = -1.956272333 Simplifying w = -1.956272333Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.622939001, -1.956272333}
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