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Simplifying -1w2 + 50w + 800 = 0 Reorder the terms: 800 + 50w + -1w2 = 0 Solving 800 + 50w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -800 + -50w + w2 = 0 Move the constant term to the right: Add '800' to each side of the equation. -800 + -50w + 800 + w2 = 0 + 800 Reorder the terms: -800 + 800 + -50w + w2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + -50w + w2 = 0 + 800 -50w + w2 = 0 + 800 Combine like terms: 0 + 800 = 800 -50w + w2 = 800 The w term is -50w. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50w + 625 + w2 = 800 + 625 Reorder the terms: 625 + -50w + w2 = 800 + 625 Combine like terms: 800 + 625 = 1425 625 + -50w + w2 = 1425 Factor a perfect square on the left side: (w + -25)(w + -25) = 1425 Calculate the square root of the right side: 37.749172176 Break this problem into two subproblems by setting (w + -25) equal to 37.749172176 and -37.749172176.Subproblem 1
w + -25 = 37.749172176 Simplifying w + -25 = 37.749172176 Reorder the terms: -25 + w = 37.749172176 Solving -25 + w = 37.749172176 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + w = 37.749172176 + 25 Combine like terms: -25 + 25 = 0 0 + w = 37.749172176 + 25 w = 37.749172176 + 25 Combine like terms: 37.749172176 + 25 = 62.749172176 w = 62.749172176 Simplifying w = 62.749172176Subproblem 2
w + -25 = -37.749172176 Simplifying w + -25 = -37.749172176 Reorder the terms: -25 + w = -37.749172176 Solving -25 + w = -37.749172176 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + w = -37.749172176 + 25 Combine like terms: -25 + 25 = 0 0 + w = -37.749172176 + 25 w = -37.749172176 + 25 Combine like terms: -37.749172176 + 25 = -12.749172176 w = -12.749172176 Simplifying w = -12.749172176Solution
The solution to the problem is based on the solutions from the subproblems. w = {62.749172176, -12.749172176}
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