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Simplifying w2 = 2 + -10w Solving w2 = 2 + -10w Solving for variable 'w'. Reorder the terms: -2 + 10w + w2 = 2 + -10w + -2 + 10w Reorder the terms: -2 + 10w + w2 = 2 + -2 + -10w + 10w Combine like terms: 2 + -2 = 0 -2 + 10w + w2 = 0 + -10w + 10w -2 + 10w + w2 = -10w + 10w Combine like terms: -10w + 10w = 0 -2 + 10w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 10w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + 10w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 10w + w2 = 0 + 2 10w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 10w + w2 = 2 The w term is 10w. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10w + 25 + w2 = 2 + 25 Reorder the terms: 25 + 10w + w2 = 2 + 25 Combine like terms: 2 + 25 = 27 25 + 10w + w2 = 27 Factor a perfect square on the left side: (w + 5)(w + 5) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (w + 5) equal to 5.196152423 and -5.196152423.Subproblem 1
w + 5 = 5.196152423 Simplifying w + 5 = 5.196152423 Reorder the terms: 5 + w = 5.196152423 Solving 5 + w = 5.196152423 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 5.196152423 + -5 Combine like terms: 5 + -5 = 0 0 + w = 5.196152423 + -5 w = 5.196152423 + -5 Combine like terms: 5.196152423 + -5 = 0.196152423 w = 0.196152423 Simplifying w = 0.196152423Subproblem 2
w + 5 = -5.196152423 Simplifying w + 5 = -5.196152423 Reorder the terms: 5 + w = -5.196152423 Solving 5 + w = -5.196152423 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = -5.196152423 + -5 Combine like terms: 5 + -5 = 0 0 + w = -5.196152423 + -5 w = -5.196152423 + -5 Combine like terms: -5.196152423 + -5 = -10.196152423 w = -10.196152423 Simplifying w = -10.196152423Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.196152423, -10.196152423}
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