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Simplifying w2 + -5w = 2.75 Reorder the terms: -5w + w2 = 2.75 Solving -5w + w2 = 2.75 Solving for variable 'w'. Reorder the terms: -2.75 + -5w + w2 = 2.75 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 -2.75 + -5w + w2 = 0.00 Begin completing the square. Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -5w + 2.75 + w2 = 0.00 + 2.75 Reorder the terms: -2.75 + 2.75 + -5w + w2 = 0.00 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -5w + w2 = 0.00 + 2.75 -5w + w2 = 0.00 + 2.75 Combine like terms: 0.00 + 2.75 = 2.75 -5w + w2 = 2.75 The w term is -5w. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5w + 6.25 + w2 = 2.75 + 6.25 Reorder the terms: 6.25 + -5w + w2 = 2.75 + 6.25 Combine like terms: 2.75 + 6.25 = 9 6.25 + -5w + w2 = 9 Factor a perfect square on the left side: (w + -2.5)(w + -2.5) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (w + -2.5) equal to 3 and -3.Subproblem 1
w + -2.5 = 3 Simplifying w + -2.5 = 3 Reorder the terms: -2.5 + w = 3 Solving -2.5 + w = 3 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + w = 3 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = 3 + 2.5 w = 3 + 2.5 Combine like terms: 3 + 2.5 = 5.5 w = 5.5 Simplifying w = 5.5Subproblem 2
w + -2.5 = -3 Simplifying w + -2.5 = -3 Reorder the terms: -2.5 + w = -3 Solving -2.5 + w = -3 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + w = -3 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = -3 + 2.5 w = -3 + 2.5 Combine like terms: -3 + 2.5 = -0.5 w = -0.5 Simplifying w = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.5, -0.5}
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