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Simplifying -4(3w + -5) + -1(2w2 + -8w + 9) = 0 Reorder the terms: -4(-5 + 3w) + -1(2w2 + -8w + 9) = 0 (-5 * -4 + 3w * -4) + -1(2w2 + -8w + 9) = 0 (20 + -12w) + -1(2w2 + -8w + 9) = 0 Reorder the terms: 20 + -12w + -1(9 + -8w + 2w2) = 0 20 + -12w + (9 * -1 + -8w * -1 + 2w2 * -1) = 0 20 + -12w + (-9 + 8w + -2w2) = 0 Reorder the terms: 20 + -9 + -12w + 8w + -2w2 = 0 Combine like terms: 20 + -9 = 11 11 + -12w + 8w + -2w2 = 0 Combine like terms: -12w + 8w = -4w 11 + -4w + -2w2 = 0 Solving 11 + -4w + -2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5.5 + 2w + w2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 2w + 5.5 + w2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 2w + w2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 2w + w2 = 0 + 5.5 2w + w2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 2w + w2 = 5.5 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 5.5 + 1 Reorder the terms: 1 + 2w + w2 = 5.5 + 1 Combine like terms: 5.5 + 1 = 6.5 1 + 2w + w2 = 6.5 Factor a perfect square on the left side: (w + 1)(w + 1) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (w + 1) equal to 2.549509757 and -2.549509757.Subproblem 1
w + 1 = 2.549509757 Simplifying w + 1 = 2.549509757 Reorder the terms: 1 + w = 2.549509757 Solving 1 + w = 2.549509757 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 2.549509757 + -1 Combine like terms: 1 + -1 = 0 0 + w = 2.549509757 + -1 w = 2.549509757 + -1 Combine like terms: 2.549509757 + -1 = 1.549509757 w = 1.549509757 Simplifying w = 1.549509757Subproblem 2
w + 1 = -2.549509757 Simplifying w + 1 = -2.549509757 Reorder the terms: 1 + w = -2.549509757 Solving 1 + w = -2.549509757 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -2.549509757 + -1 Combine like terms: 1 + -1 = 0 0 + w = -2.549509757 + -1 w = -2.549509757 + -1 Combine like terms: -2.549509757 + -1 = -3.549509757 w = -3.549509757 Simplifying w = -3.549509757Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.549509757, -3.549509757}
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