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Simplifying w2 + 25w + -750 = 0 Reorder the terms: -750 + 25w + w2 = 0 Solving -750 + 25w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '750' to each side of the equation. -750 + 25w + 750 + w2 = 0 + 750 Reorder the terms: -750 + 750 + 25w + w2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + 25w + w2 = 0 + 750 25w + w2 = 0 + 750 Combine like terms: 0 + 750 = 750 25w + w2 = 750 The w term is 25w. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25w + 156.25 + w2 = 750 + 156.25 Reorder the terms: 156.25 + 25w + w2 = 750 + 156.25 Combine like terms: 750 + 156.25 = 906.25 156.25 + 25w + w2 = 906.25 Factor a perfect square on the left side: (w + 12.5)(w + 12.5) = 906.25 Calculate the square root of the right side: 30.103986447 Break this problem into two subproblems by setting (w + 12.5) equal to 30.103986447 and -30.103986447.Subproblem 1
w + 12.5 = 30.103986447 Simplifying w + 12.5 = 30.103986447 Reorder the terms: 12.5 + w = 30.103986447 Solving 12.5 + w = 30.103986447 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + w = 30.103986447 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + w = 30.103986447 + -12.5 w = 30.103986447 + -12.5 Combine like terms: 30.103986447 + -12.5 = 17.603986447 w = 17.603986447 Simplifying w = 17.603986447Subproblem 2
w + 12.5 = -30.103986447 Simplifying w + 12.5 = -30.103986447 Reorder the terms: 12.5 + w = -30.103986447 Solving 12.5 + w = -30.103986447 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + w = -30.103986447 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + w = -30.103986447 + -12.5 w = -30.103986447 + -12.5 Combine like terms: -30.103986447 + -12.5 = -42.603986447 w = -42.603986447 Simplifying w = -42.603986447Solution
The solution to the problem is based on the solutions from the subproblems. w = {17.603986447, -42.603986447}
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