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Simplifying 2w2 + 15w + -37 = 0 Reorder the terms: -37 + 15w + 2w2 = 0 Solving -37 + 15w + 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'. -18.5 + 7.5w + w2 = 0 Move the constant term to the right: Add '18.5' to each side of the equation. -18.5 + 7.5w + 18.5 + w2 = 0 + 18.5 Reorder the terms: -18.5 + 18.5 + 7.5w + w2 = 0 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + 7.5w + w2 = 0 + 18.5 7.5w + w2 = 0 + 18.5 Combine like terms: 0 + 18.5 = 18.5 7.5w + w2 = 18.5 The w term is 7.5w. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5w + 14.0625 + w2 = 18.5 + 14.0625 Reorder the terms: 14.0625 + 7.5w + w2 = 18.5 + 14.0625 Combine like terms: 18.5 + 14.0625 = 32.5625 14.0625 + 7.5w + w2 = 32.5625 Factor a perfect square on the left side: (w + 3.75)(w + 3.75) = 32.5625 Calculate the square root of the right side: 5.706356105 Break this problem into two subproblems by setting (w + 3.75) equal to 5.706356105 and -5.706356105.Subproblem 1
w + 3.75 = 5.706356105 Simplifying w + 3.75 = 5.706356105 Reorder the terms: 3.75 + w = 5.706356105 Solving 3.75 + w = 5.706356105 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + w = 5.706356105 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + w = 5.706356105 + -3.75 w = 5.706356105 + -3.75 Combine like terms: 5.706356105 + -3.75 = 1.956356105 w = 1.956356105 Simplifying w = 1.956356105Subproblem 2
w + 3.75 = -5.706356105 Simplifying w + 3.75 = -5.706356105 Reorder the terms: 3.75 + w = -5.706356105 Solving 3.75 + w = -5.706356105 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + w = -5.706356105 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + w = -5.706356105 + -3.75 w = -5.706356105 + -3.75 Combine like terms: -5.706356105 + -3.75 = -9.456356105 w = -9.456356105 Simplifying w = -9.456356105Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.956356105, -9.456356105}
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