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Simplifying 2w2 + 5w = 36 Reorder the terms: 5w + 2w2 = 36 Solving 5w + 2w2 = 36 Solving for variable 'w'. Reorder the terms: -36 + 5w + 2w2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 5w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18 + 2.5w + w2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 2.5w + 18 + w2 = 0 + 18 Reorder the terms: -18 + 18 + 2.5w + w2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 2.5w + w2 = 0 + 18 2.5w + w2 = 0 + 18 Combine like terms: 0 + 18 = 18 2.5w + w2 = 18 The w term is 2.5w. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5w + 1.5625 + w2 = 18 + 1.5625 Reorder the terms: 1.5625 + 2.5w + w2 = 18 + 1.5625 Combine like terms: 18 + 1.5625 = 19.5625 1.5625 + 2.5w + w2 = 19.5625 Factor a perfect square on the left side: (w + 1.25)(w + 1.25) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (w + 1.25) equal to 4.422951503 and -4.422951503.Subproblem 1
w + 1.25 = 4.422951503 Simplifying w + 1.25 = 4.422951503 Reorder the terms: 1.25 + w = 4.422951503 Solving 1.25 + w = 4.422951503 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = 4.422951503 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = 4.422951503 + -1.25 w = 4.422951503 + -1.25 Combine like terms: 4.422951503 + -1.25 = 3.172951503 w = 3.172951503 Simplifying w = 3.172951503Subproblem 2
w + 1.25 = -4.422951503 Simplifying w + 1.25 = -4.422951503 Reorder the terms: 1.25 + w = -4.422951503 Solving 1.25 + w = -4.422951503 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = -4.422951503 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = -4.422951503 + -1.25 w = -4.422951503 + -1.25 Combine like terms: -4.422951503 + -1.25 = -5.672951503 w = -5.672951503 Simplifying w = -5.672951503Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.172951503, -5.672951503}
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