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Simplifying (4w2 + -6w + -1) + (3w2 + -7w + 5) = 0 Reorder the terms: (-1 + -6w + 4w2) + (3w2 + -7w + 5) = 0 Remove parenthesis around (-1 + -6w + 4w2) -1 + -6w + 4w2 + (3w2 + -7w + 5) = 0 Reorder the terms: -1 + -6w + 4w2 + (5 + -7w + 3w2) = 0 Remove parenthesis around (5 + -7w + 3w2) -1 + -6w + 4w2 + 5 + -7w + 3w2 = 0 Reorder the terms: -1 + 5 + -6w + -7w + 4w2 + 3w2 = 0 Combine like terms: -1 + 5 = 4 4 + -6w + -7w + 4w2 + 3w2 = 0 Combine like terms: -6w + -7w = -13w 4 + -13w + 4w2 + 3w2 = 0 Combine like terms: 4w2 + 3w2 = 7w2 4 + -13w + 7w2 = 0 Solving 4 + -13w + 7w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + -1.857142857w + w2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -1.857142857w + -0.5714285714 + w2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -1.857142857w + w2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -1.857142857w + w2 = 0 + -0.5714285714 -1.857142857w + w2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -1.857142857w + w2 = -0.5714285714 The w term is -1.857142857w. Take half its coefficient (-0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. -1.857142857w + 0.8622448978 + w2 = -0.5714285714 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857w + w2 = -0.5714285714 + 0.8622448978 Combine like terms: -0.5714285714 + 0.8622448978 = 0.2908163264 0.8622448978 + -1.857142857w + w2 = 0.2908163264 Factor a perfect square on the left side: (w + -0.9285714285)(w + -0.9285714285) = 0.2908163264 Calculate the square root of the right side: 0.539273888 Break this problem into two subproblems by setting (w + -0.9285714285) equal to 0.539273888 and -0.539273888.Subproblem 1
w + -0.9285714285 = 0.539273888 Simplifying w + -0.9285714285 = 0.539273888 Reorder the terms: -0.9285714285 + w = 0.539273888 Solving -0.9285714285 + w = 0.539273888 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + w = 0.539273888 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + w = 0.539273888 + 0.9285714285 w = 0.539273888 + 0.9285714285 Combine like terms: 0.539273888 + 0.9285714285 = 1.4678453165 w = 1.4678453165 Simplifying w = 1.4678453165Subproblem 2
w + -0.9285714285 = -0.539273888 Simplifying w + -0.9285714285 = -0.539273888 Reorder the terms: -0.9285714285 + w = -0.539273888 Solving -0.9285714285 + w = -0.539273888 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + w = -0.539273888 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + w = -0.539273888 + 0.9285714285 w = -0.539273888 + 0.9285714285 Combine like terms: -0.539273888 + 0.9285714285 = 0.3892975405 w = 0.3892975405 Simplifying w = 0.3892975405Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.4678453165, 0.3892975405}
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