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Simplifying w2 + 13w + 36 = 100 Reorder the terms: 36 + 13w + w2 = 100 Solving 36 + 13w + w2 = 100 Solving for variable 'w'. Reorder the terms: 36 + -100 + 13w + w2 = 100 + -100 Combine like terms: 36 + -100 = -64 -64 + 13w + w2 = 100 + -100 Combine like terms: 100 + -100 = 0 -64 + 13w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 13w + 64 + w2 = 0 + 64 Reorder the terms: -64 + 64 + 13w + w2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 13w + w2 = 0 + 64 13w + w2 = 0 + 64 Combine like terms: 0 + 64 = 64 13w + w2 = 64 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 = 64 + 42.25 Reorder the terms: 42.25 + 13w + w2 = 64 + 42.25 Combine like terms: 64 + 42.25 = 106.25 42.25 + 13w + w2 = 106.25 Factor a perfect square on the left side: (w + 6.5)(w + 6.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (w + 6.5) equal to 10.307764064 and -10.307764064.Subproblem 1
w + 6.5 = 10.307764064 Simplifying w + 6.5 = 10.307764064 Reorder the terms: 6.5 + w = 10.307764064 Solving 6.5 + w = 10.307764064 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 = 10.307764064 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + w = 10.307764064 + -6.5 w = 10.307764064 + -6.5 Combine like terms: 10.307764064 + -6.5 = 3.807764064 w = 3.807764064 Simplifying w = 3.807764064Subproblem 2
w + 6.5 = -10.307764064 Simplifying w + 6.5 = -10.307764064 Reorder the terms: 6.5 + w = -10.307764064 Solving 6.5 + w = -10.307764064 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 = -10.307764064 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + w = -10.307764064 + -6.5 w = -10.307764064 + -6.5 Combine like terms: -10.307764064 + -6.5 = -16.807764064 w = -16.807764064 Simplifying w = -16.807764064Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.807764064, -16.807764064}
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