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Simplifying w2 + 13w + 4 = 0 Reorder the terms: 4 + 13w + w2 = 0 Solving 4 + 13w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 13w + -4 + w2 = 0 + -4 Reorder the terms: 4 + -4 + 13w + w2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 13w + w2 = 0 + -4 13w + w2 = 0 + -4 Combine like terms: 0 + -4 = -4 13w + w2 = -4 The w term is 13w. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13w + 42.25 + w2 = -4 + 42.25 Reorder the terms: 42.25 + 13w + w2 = -4 + 42.25 Combine like terms: -4 + 42.25 = 38.25 42.25 + 13w + w2 = 38.25 Factor a perfect square on the left side: (w + 6.5)(w + 6.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (w + 6.5) equal to 6.184658438 and -6.184658438.Subproblem 1
w + 6.5 = 6.184658438 Simplifying w + 6.5 = 6.184658438 Reorder the terms: 6.5 + w = 6.184658438 Solving 6.5 + w = 6.184658438 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + w = 6.184658438 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + w = 6.184658438 + -6.5 w = 6.184658438 + -6.5 Combine like terms: 6.184658438 + -6.5 = -0.315341562 w = -0.315341562 Simplifying w = -0.315341562Subproblem 2
w + 6.5 = -6.184658438 Simplifying w + 6.5 = -6.184658438 Reorder the terms: 6.5 + w = -6.184658438 Solving 6.5 + w = -6.184658438 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + w = -6.184658438 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + w = -6.184658438 + -6.5 w = -6.184658438 + -6.5 Combine like terms: -6.184658438 + -6.5 = -12.684658438 w = -12.684658438 Simplifying w = -12.684658438Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.315341562, -12.684658438}
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