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Simplifying w2 + 6w + c = 130 + c Reorder the terms: c + 6w + w2 = 130 + c Add '-1c' to each side of the equation. c + 6w + -1c + w2 = 130 + c + -1c Reorder the terms: c + -1c + 6w + w2 = 130 + c + -1c Combine like terms: c + -1c = 0 0 + 6w + w2 = 130 + c + -1c 6w + w2 = 130 + c + -1c Combine like terms: c + -1c = 0 6w + w2 = 130 + 0 6w + w2 = 130 Solving 6w + w2 = 130 Solving for variable 'w'. Reorder the terms: -130 + 6w + w2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 6w + 130 + w2 = 0 + 130 Reorder the terms: -130 + 130 + 6w + w2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 6w + w2 = 0 + 130 6w + w2 = 0 + 130 Combine like terms: 0 + 130 = 130 6w + w2 = 130 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 130 + 9 Reorder the terms: 9 + 6w + w2 = 130 + 9 Combine like terms: 130 + 9 = 139 9 + 6w + w2 = 139 Factor a perfect square on the left side: (w + 3)(w + 3) = 139 Calculate the square root of the right side: 11.789826123 Break this problem into two subproblems by setting (w + 3) equal to 11.789826123 and -11.789826123.Subproblem 1
w + 3 = 11.789826123 Simplifying w + 3 = 11.789826123 Reorder the terms: 3 + w = 11.789826123 Solving 3 + w = 11.789826123 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 11.789826123 + -3 Combine like terms: 3 + -3 = 0 0 + w = 11.789826123 + -3 w = 11.789826123 + -3 Combine like terms: 11.789826123 + -3 = 8.789826123 w = 8.789826123 Simplifying w = 8.789826123Subproblem 2
w + 3 = -11.789826123 Simplifying w + 3 = -11.789826123 Reorder the terms: 3 + w = -11.789826123 Solving 3 + w = -11.789826123 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -11.789826123 + -3 Combine like terms: 3 + -3 = 0 0 + w = -11.789826123 + -3 w = -11.789826123 + -3 Combine like terms: -11.789826123 + -3 = -14.789826123 w = -14.789826123 Simplifying w = -14.789826123Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.789826123, -14.789826123}
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