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Simplifying 4w2 + 20w + -41 = 0 Reorder the terms: -41 + 20w + 4w2 = 0 Solving -41 + 20w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.25 + 5w + w2 = 0 Move the constant term to the right: Add '10.25' to each side of the equation. -10.25 + 5w + 10.25 + w2 = 0 + 10.25 Reorder the terms: -10.25 + 10.25 + 5w + w2 = 0 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + 5w + w2 = 0 + 10.25 5w + w2 = 0 + 10.25 Combine like terms: 0 + 10.25 = 10.25 5w + w2 = 10.25 The w term is 5w. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5w + 6.25 + w2 = 10.25 + 6.25 Reorder the terms: 6.25 + 5w + w2 = 10.25 + 6.25 Combine like terms: 10.25 + 6.25 = 16.5 6.25 + 5w + w2 = 16.5 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (w + 2.5) equal to 4.062019202 and -4.062019202.Subproblem 1
w + 2.5 = 4.062019202 Simplifying w + 2.5 = 4.062019202 Reorder the terms: 2.5 + w = 4.062019202 Solving 2.5 + w = 4.062019202 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 4.062019202 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 4.062019202 + -2.5 w = 4.062019202 + -2.5 Combine like terms: 4.062019202 + -2.5 = 1.562019202 w = 1.562019202 Simplifying w = 1.562019202Subproblem 2
w + 2.5 = -4.062019202 Simplifying w + 2.5 = -4.062019202 Reorder the terms: 2.5 + w = -4.062019202 Solving 2.5 + w = -4.062019202 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -4.062019202 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -4.062019202 + -2.5 w = -4.062019202 + -2.5 Combine like terms: -4.062019202 + -2.5 = -6.562019202 w = -6.562019202 Simplifying w = -6.562019202Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.562019202, -6.562019202}
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