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Simplifying 2w2 + 29w + -286 = 0 Reorder the terms: -286 + 29w + 2w2 = 0 Solving -286 + 29w + 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'. -143 + 14.5w + w2 = 0 Move the constant term to the right: Add '143' to each side of the equation. -143 + 14.5w + 143 + w2 = 0 + 143 Reorder the terms: -143 + 143 + 14.5w + w2 = 0 + 143 Combine like terms: -143 + 143 = 0 0 + 14.5w + w2 = 0 + 143 14.5w + w2 = 0 + 143 Combine like terms: 0 + 143 = 143 14.5w + w2 = 143 The w term is 14.5w. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5w + 52.5625 + w2 = 143 + 52.5625 Reorder the terms: 52.5625 + 14.5w + w2 = 143 + 52.5625 Combine like terms: 143 + 52.5625 = 195.5625 52.5625 + 14.5w + w2 = 195.5625 Factor a perfect square on the left side: (w + 7.25)(w + 7.25) = 195.5625 Calculate the square root of the right side: 13.984366271 Break this problem into two subproblems by setting (w + 7.25) equal to 13.984366271 and -13.984366271.Subproblem 1
w + 7.25 = 13.984366271 Simplifying w + 7.25 = 13.984366271 Reorder the terms: 7.25 + w = 13.984366271 Solving 7.25 + w = 13.984366271 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + w = 13.984366271 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + w = 13.984366271 + -7.25 w = 13.984366271 + -7.25 Combine like terms: 13.984366271 + -7.25 = 6.734366271 w = 6.734366271 Simplifying w = 6.734366271Subproblem 2
w + 7.25 = -13.984366271 Simplifying w + 7.25 = -13.984366271 Reorder the terms: 7.25 + w = -13.984366271 Solving 7.25 + w = -13.984366271 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + w = -13.984366271 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + w = -13.984366271 + -7.25 w = -13.984366271 + -7.25 Combine like terms: -13.984366271 + -7.25 = -21.234366271 w = -21.234366271 Simplifying w = -21.234366271Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.734366271, -21.234366271}
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