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Simplifying 3w2 + -75w + 25 = 0 Reorder the terms: 25 + -75w + 3w2 = 0 Solving 25 + -75w + 3w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8.333333333 + -25w + w2 = 0 Move the constant term to the right: Add '-8.333333333' to each side of the equation. 8.333333333 + -25w + -8.333333333 + w2 = 0 + -8.333333333 Reorder the terms: 8.333333333 + -8.333333333 + -25w + w2 = 0 + -8.333333333 Combine like terms: 8.333333333 + -8.333333333 = 0.000000000 0.000000000 + -25w + w2 = 0 + -8.333333333 -25w + w2 = 0 + -8.333333333 Combine like terms: 0 + -8.333333333 = -8.333333333 -25w + w2 = -8.333333333 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 = -8.333333333 + 156.25 Reorder the terms: 156.25 + -25w + w2 = -8.333333333 + 156.25 Combine like terms: -8.333333333 + 156.25 = 147.916666667 156.25 + -25w + w2 = 147.916666667 Factor a perfect square on the left side: (w + -12.5)(w + -12.5) = 147.916666667 Calculate the square root of the right side: 12.162099599 Break this problem into two subproblems by setting (w + -12.5) equal to 12.162099599 and -12.162099599.Subproblem 1
w + -12.5 = 12.162099599 Simplifying w + -12.5 = 12.162099599 Reorder the terms: -12.5 + w = 12.162099599 Solving -12.5 + w = 12.162099599 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 = 12.162099599 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + w = 12.162099599 + 12.5 w = 12.162099599 + 12.5 Combine like terms: 12.162099599 + 12.5 = 24.662099599 w = 24.662099599 Simplifying w = 24.662099599Subproblem 2
w + -12.5 = -12.162099599 Simplifying w + -12.5 = -12.162099599 Reorder the terms: -12.5 + w = -12.162099599 Solving -12.5 + w = -12.162099599 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 = -12.162099599 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + w = -12.162099599 + 12.5 w = -12.162099599 + 12.5 Combine like terms: -12.162099599 + 12.5 = 0.337900401 w = 0.337900401 Simplifying w = 0.337900401Solution
The solution to the problem is based on the solutions from the subproblems. w = {24.662099599, 0.337900401}
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