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Simplifying (6 + w)(w + 10) = 160 Reorder the terms: (6 + w)(10 + w) = 160 Multiply (6 + w) * (10 + w) (6(10 + w) + w(10 + w)) = 160 ((10 * 6 + w * 6) + w(10 + w)) = 160 ((60 + 6w) + w(10 + w)) = 160 (60 + 6w + (10 * w + w * w)) = 160 (60 + 6w + (10w + w2)) = 160 Combine like terms: 6w + 10w = 16w (60 + 16w + w2) = 160 Solving 60 + 16w + w2 = 160 Solving for variable 'w'. Reorder the terms: 60 + -160 + 16w + w2 = 160 + -160 Combine like terms: 60 + -160 = -100 -100 + 16w + w2 = 160 + -160 Combine like terms: 160 + -160 = 0 -100 + 16w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 16w + 100 + w2 = 0 + 100 Reorder the terms: -100 + 100 + 16w + w2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 16w + w2 = 0 + 100 16w + w2 = 0 + 100 Combine like terms: 0 + 100 = 100 16w + w2 = 100 The w term is 16w. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16w + 64 + w2 = 100 + 64 Reorder the terms: 64 + 16w + w2 = 100 + 64 Combine like terms: 100 + 64 = 164 64 + 16w + w2 = 164 Factor a perfect square on the left side: (w + 8)(w + 8) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (w + 8) equal to 12.806248475 and -12.806248475.Subproblem 1
w + 8 = 12.806248475 Simplifying w + 8 = 12.806248475 Reorder the terms: 8 + w = 12.806248475 Solving 8 + w = 12.806248475 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = 12.806248475 + -8 Combine like terms: 8 + -8 = 0 0 + w = 12.806248475 + -8 w = 12.806248475 + -8 Combine like terms: 12.806248475 + -8 = 4.806248475 w = 4.806248475 Simplifying w = 4.806248475Subproblem 2
w + 8 = -12.806248475 Simplifying w + 8 = -12.806248475 Reorder the terms: 8 + w = -12.806248475 Solving 8 + w = -12.806248475 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = -12.806248475 + -8 Combine like terms: 8 + -8 = 0 0 + w = -12.806248475 + -8 w = -12.806248475 + -8 Combine like terms: -12.806248475 + -8 = -20.806248475 w = -20.806248475 Simplifying w = -20.806248475Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.806248475, -20.806248475}
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