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Simplifying 49w2 + 56w + 1 = 0 Reorder the terms: 1 + 56w + 49w2 = 0 Solving 1 + 56w + 49w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.02040816327 + 1.142857143w + w2 = 0 Move the constant term to the right: Add '-0.02040816327' to each side of the equation. 0.02040816327 + 1.142857143w + -0.02040816327 + w2 = 0 + -0.02040816327 Reorder the terms: 0.02040816327 + -0.02040816327 + 1.142857143w + w2 = 0 + -0.02040816327 Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000 0.00000000000 + 1.142857143w + w2 = 0 + -0.02040816327 1.142857143w + w2 = 0 + -0.02040816327 Combine like terms: 0 + -0.02040816327 = -0.02040816327 1.142857143w + w2 = -0.02040816327 The w term is 1.142857143w. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143w + 0.3265306123 + w2 = -0.02040816327 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143w + w2 = -0.02040816327 + 0.3265306123 Combine like terms: -0.02040816327 + 0.3265306123 = 0.30612244903 0.3265306123 + 1.142857143w + w2 = 0.30612244903 Factor a perfect square on the left side: (w + 0.5714285715)(w + 0.5714285715) = 0.30612244903 Calculate the square root of the right side: 0.553283335 Break this problem into two subproblems by setting (w + 0.5714285715) equal to 0.553283335 and -0.553283335.Subproblem 1
w + 0.5714285715 = 0.553283335 Simplifying w + 0.5714285715 = 0.553283335 Reorder the terms: 0.5714285715 + w = 0.553283335 Solving 0.5714285715 + w = 0.553283335 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + w = 0.553283335 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + w = 0.553283335 + -0.5714285715 w = 0.553283335 + -0.5714285715 Combine like terms: 0.553283335 + -0.5714285715 = -0.0181452365 w = -0.0181452365 Simplifying w = -0.0181452365Subproblem 2
w + 0.5714285715 = -0.553283335 Simplifying w + 0.5714285715 = -0.553283335 Reorder the terms: 0.5714285715 + w = -0.553283335 Solving 0.5714285715 + w = -0.553283335 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + w = -0.553283335 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + w = -0.553283335 + -0.5714285715 w = -0.553283335 + -0.5714285715 Combine like terms: -0.553283335 + -0.5714285715 = -1.1247119065 w = -1.1247119065 Simplifying w = -1.1247119065Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.0181452365, -1.1247119065}
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