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Simplifying w2 + -7w + 2 = 0 Reorder the terms: 2 + -7w + w2 = 0 Solving 2 + -7w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -7w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + -7w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7w + w2 = 0 + -2 -7w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 -7w + w2 = -2 The w term is -7w. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7w + 12.25 + w2 = -2 + 12.25 Reorder the terms: 12.25 + -7w + w2 = -2 + 12.25 Combine like terms: -2 + 12.25 = 10.25 12.25 + -7w + w2 = 10.25 Factor a perfect square on the left side: (w + -3.5)(w + -3.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (w + -3.5) equal to 3.201562119 and -3.201562119.Subproblem 1
w + -3.5 = 3.201562119 Simplifying w + -3.5 = 3.201562119 Reorder the terms: -3.5 + w = 3.201562119 Solving -3.5 + w = 3.201562119 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + w = 3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + w = 3.201562119 + 3.5 w = 3.201562119 + 3.5 Combine like terms: 3.201562119 + 3.5 = 6.701562119 w = 6.701562119 Simplifying w = 6.701562119Subproblem 2
w + -3.5 = -3.201562119 Simplifying w + -3.5 = -3.201562119 Reorder the terms: -3.5 + w = -3.201562119 Solving -3.5 + w = -3.201562119 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + w = -3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + w = -3.201562119 + 3.5 w = -3.201562119 + 3.5 Combine like terms: -3.201562119 + 3.5 = 0.298437881 w = 0.298437881 Simplifying w = 0.298437881Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.701562119, 0.298437881}
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