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Simplifying 6w2 + 13w + -4 = 0 Reorder the terms: -4 + 13w + 6w2 = 0 Solving -4 + 13w + 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'. -0.6666666667 + 2.166666667w + w2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 2.166666667w + 0.6666666667 + w2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 2.166666667w + w2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 2.166666667w + w2 = 0 + 0.6666666667 2.166666667w + w2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 2.166666667w + w2 = 0.6666666667 The w term is 2.166666667w. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667w + 1.173611113 + w2 = 0.6666666667 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667w + w2 = 0.6666666667 + 1.173611113 Combine like terms: 0.6666666667 + 1.173611113 = 1.8402777797 1.173611113 + 2.166666667w + w2 = 1.8402777797 Factor a perfect square on the left side: (w + 1.083333334)(w + 1.083333334) = 1.8402777797 Calculate the square root of the right side: 1.356568384 Break this problem into two subproblems by setting (w + 1.083333334) equal to 1.356568384 and -1.356568384.Subproblem 1
w + 1.083333334 = 1.356568384 Simplifying w + 1.083333334 = 1.356568384 Reorder the terms: 1.083333334 + w = 1.356568384 Solving 1.083333334 + w = 1.356568384 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + w = 1.356568384 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + w = 1.356568384 + -1.083333334 w = 1.356568384 + -1.083333334 Combine like terms: 1.356568384 + -1.083333334 = 0.27323505 w = 0.27323505 Simplifying w = 0.27323505Subproblem 2
w + 1.083333334 = -1.356568384 Simplifying w + 1.083333334 = -1.356568384 Reorder the terms: 1.083333334 + w = -1.356568384 Solving 1.083333334 + w = -1.356568384 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + w = -1.356568384 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + w = -1.356568384 + -1.083333334 w = -1.356568384 + -1.083333334 Combine like terms: -1.356568384 + -1.083333334 = -2.439901718 w = -2.439901718 Simplifying w = -2.439901718Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.27323505, -2.439901718}
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