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Simplifying (4w2) + -1(3w) + -1(6) = 0 Remove parenthesis around (3w) (4w2) + -1 * 3w + -1(6) = 0 Multiply -1 * 3 (4w2) + -3w + -1(6) = 0 Multiply -1 * 6 (4w2) + -3w + -6 = 0 Reorder the terms: -6 + -3w + (4w2) = 0 Solving -6 + -3w + (4w2) = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -0.75w + w2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.75w + 1.5 + w2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.75w + w2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.75w + w2 = 0 + 1.5 -0.75w + w2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.75w + w2 = 1.5 The w term is -0.75w. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75w + 0.140625 + w2 = 1.5 + 0.140625 Reorder the terms: 0.140625 + -0.75w + w2 = 1.5 + 0.140625 Combine like terms: 1.5 + 0.140625 = 1.640625 0.140625 + -0.75w + w2 = 1.640625 Factor a perfect square on the left side: ((w) + -0.375)((w) + -0.375) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting ((w) + -0.375) equal to 1.280868846 and -1.280868846.Subproblem 1
(w) + -0.375 = 1.280868846 Simplifying (w) + -0.375 = 1.280868846 w + -0.375 = 1.280868846 Reorder the terms: -0.375 + w = 1.280868846 Solving -0.375 + w = 1.280868846 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + w = 1.280868846 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + w = 1.280868846 + 0.375 w = 1.280868846 + 0.375 Combine like terms: 1.280868846 + 0.375 = 1.655868846 w = 1.655868846 Simplifying w = 1.655868846Subproblem 2
(w) + -0.375 = -1.280868846 Simplifying (w) + -0.375 = -1.280868846 w + -0.375 = -1.280868846 Reorder the terms: -0.375 + w = -1.280868846 Solving -0.375 + w = -1.280868846 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + w = -1.280868846 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + w = -1.280868846 + 0.375 w = -1.280868846 + 0.375 Combine like terms: -1.280868846 + 0.375 = -0.905868846 w = -0.905868846 Simplifying w = -0.905868846Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.655868846, -0.905868846}
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