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Simplifying 0 = -1w2 + 25w + 500 Reorder the terms: 0 = 500 + 25w + -1w2 Solving 0 = 500 + 25w + -1w2 Solving for variable 'w'. Combine like terms: 0 + -500 = -500 -500 + -25w + w2 = 500 + 25w + -1w2 + -500 + -25w + w2 Reorder the terms: -500 + -25w + w2 = 500 + -500 + 25w + -25w + -1w2 + w2 Combine like terms: 500 + -500 = 0 -500 + -25w + w2 = 0 + 25w + -25w + -1w2 + w2 -500 + -25w + w2 = 25w + -25w + -1w2 + w2 Combine like terms: 25w + -25w = 0 -500 + -25w + w2 = 0 + -1w2 + w2 -500 + -25w + w2 = -1w2 + w2 Combine like terms: -1w2 + w2 = 0 -500 + -25w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + -25w + 500 + w2 = 0 + 500 Reorder the terms: -500 + 500 + -25w + w2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -25w + w2 = 0 + 500 -25w + w2 = 0 + 500 Combine like terms: 0 + 500 = 500 -25w + w2 = 500 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 = 500 + 156.25 Reorder the terms: 156.25 + -25w + w2 = 500 + 156.25 Combine like terms: 500 + 156.25 = 656.25 156.25 + -25w + w2 = 656.25 Factor a perfect square on the left side: (w + -12.5)(w + -12.5) = 656.25 Calculate the square root of the right side: 25.617376915 Break this problem into two subproblems by setting (w + -12.5) equal to 25.617376915 and -25.617376915.Subproblem 1
w + -12.5 = 25.617376915 Simplifying w + -12.5 = 25.617376915 Reorder the terms: -12.5 + w = 25.617376915 Solving -12.5 + w = 25.617376915 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 = 25.617376915 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + w = 25.617376915 + 12.5 w = 25.617376915 + 12.5 Combine like terms: 25.617376915 + 12.5 = 38.117376915 w = 38.117376915 Simplifying w = 38.117376915Subproblem 2
w + -12.5 = -25.617376915 Simplifying w + -12.5 = -25.617376915 Reorder the terms: -12.5 + w = -25.617376915 Solving -12.5 + w = -25.617376915 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 = -25.617376915 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + w = -25.617376915 + 12.5 w = -25.617376915 + 12.5 Combine like terms: -25.617376915 + 12.5 = -13.117376915 w = -13.117376915 Simplifying w = -13.117376915Solution
The solution to the problem is based on the solutions from the subproblems. w = {38.117376915, -13.117376915}
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