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Simplifying (w2 + -4w + -1) + (-5 + 5w2 + -3w) = 0 Reorder the terms: (-1 + -4w + w2) + (-5 + 5w2 + -3w) = 0 Remove parenthesis around (-1 + -4w + w2) -1 + -4w + w2 + (-5 + 5w2 + -3w) = 0 Reorder the terms: -1 + -4w + w2 + (-5 + -3w + 5w2) = 0 Remove parenthesis around (-5 + -3w + 5w2) -1 + -4w + w2 + -5 + -3w + 5w2 = 0 Reorder the terms: -1 + -5 + -4w + -3w + w2 + 5w2 = 0 Combine like terms: -1 + -5 = -6 -6 + -4w + -3w + w2 + 5w2 = 0 Combine like terms: -4w + -3w = -7w -6 + -7w + w2 + 5w2 = 0 Combine like terms: w2 + 5w2 = 6w2 -6 + -7w + 6w2 = 0 Solving -6 + -7w + 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 + -1.166666667w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.166666667w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -1.166666667w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.166666667w + w2 = 0 + 1 -1.166666667w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.166666667w + w2 = 1 The w term is -1.166666667w. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667w + 0.3402777780 + w2 = 1 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667w + w2 = 1 + 0.3402777780 Combine like terms: 1 + 0.3402777780 = 1.340277778 0.3402777780 + -1.166666667w + w2 = 1.340277778 Factor a perfect square on the left side: (w + -0.5833333335)(w + -0.5833333335) = 1.340277778 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (w + -0.5833333335) equal to 1.157703666 and -1.157703666.Subproblem 1
w + -0.5833333335 = 1.157703666 Simplifying w + -0.5833333335 = 1.157703666 Reorder the terms: -0.5833333335 + w = 1.157703666 Solving -0.5833333335 + w = 1.157703666 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + w = 1.157703666 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + w = 1.157703666 + 0.5833333335 w = 1.157703666 + 0.5833333335 Combine like terms: 1.157703666 + 0.5833333335 = 1.7410369995 w = 1.7410369995 Simplifying w = 1.7410369995Subproblem 2
w + -0.5833333335 = -1.157703666 Simplifying w + -0.5833333335 = -1.157703666 Reorder the terms: -0.5833333335 + w = -1.157703666 Solving -0.5833333335 + w = -1.157703666 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + w = -1.157703666 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + w = -1.157703666 + 0.5833333335 w = -1.157703666 + 0.5833333335 Combine like terms: -1.157703666 + 0.5833333335 = -0.5743703325 w = -0.5743703325 Simplifying w = -0.5743703325Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.7410369995, -0.5743703325}
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