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Simplifying w2 + -4w = 350 Reorder the terms: -4w + w2 = 350 Solving -4w + w2 = 350 Solving for variable 'w'. Reorder the terms: -350 + -4w + w2 = 350 + -350 Combine like terms: 350 + -350 = 0 -350 + -4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '350' to each side of the equation. -350 + -4w + 350 + w2 = 0 + 350 Reorder the terms: -350 + 350 + -4w + w2 = 0 + 350 Combine like terms: -350 + 350 = 0 0 + -4w + w2 = 0 + 350 -4w + w2 = 0 + 350 Combine like terms: 0 + 350 = 350 -4w + w2 = 350 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 350 + 4 Reorder the terms: 4 + -4w + w2 = 350 + 4 Combine like terms: 350 + 4 = 354 4 + -4w + w2 = 354 Factor a perfect square on the left side: (w + -2)(w + -2) = 354 Calculate the square root of the right side: 18.814887722 Break this problem into two subproblems by setting (w + -2) equal to 18.814887722 and -18.814887722.Subproblem 1
w + -2 = 18.814887722 Simplifying w + -2 = 18.814887722 Reorder the terms: -2 + w = 18.814887722 Solving -2 + w = 18.814887722 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 18.814887722 + 2 Combine like terms: -2 + 2 = 0 0 + w = 18.814887722 + 2 w = 18.814887722 + 2 Combine like terms: 18.814887722 + 2 = 20.814887722 w = 20.814887722 Simplifying w = 20.814887722Subproblem 2
w + -2 = -18.814887722 Simplifying w + -2 = -18.814887722 Reorder the terms: -2 + w = -18.814887722 Solving -2 + w = -18.814887722 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -18.814887722 + 2 Combine like terms: -2 + 2 = 0 0 + w = -18.814887722 + 2 w = -18.814887722 + 2 Combine like terms: -18.814887722 + 2 = -16.814887722 w = -16.814887722 Simplifying w = -16.814887722Solution
The solution to the problem is based on the solutions from the subproblems. w = {20.814887722, -16.814887722}
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