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Simplifying w2 + 12w + -270 = 0 Reorder the terms: -270 + 12w + w2 = 0 Solving -270 + 12w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + 12w + 270 + w2 = 0 + 270 Reorder the terms: -270 + 270 + 12w + w2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + 12w + w2 = 0 + 270 12w + w2 = 0 + 270 Combine like terms: 0 + 270 = 270 12w + w2 = 270 The w term is 12w. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12w + 36 + w2 = 270 + 36 Reorder the terms: 36 + 12w + w2 = 270 + 36 Combine like terms: 270 + 36 = 306 36 + 12w + w2 = 306 Factor a perfect square on the left side: (w + 6)(w + 6) = 306 Calculate the square root of the right side: 17.492855685 Break this problem into two subproblems by setting (w + 6) equal to 17.492855685 and -17.492855685.Subproblem 1
w + 6 = 17.492855685 Simplifying w + 6 = 17.492855685 Reorder the terms: 6 + w = 17.492855685 Solving 6 + w = 17.492855685 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + w = 17.492855685 + -6 Combine like terms: 6 + -6 = 0 0 + w = 17.492855685 + -6 w = 17.492855685 + -6 Combine like terms: 17.492855685 + -6 = 11.492855685 w = 11.492855685 Simplifying w = 11.492855685Subproblem 2
w + 6 = -17.492855685 Simplifying w + 6 = -17.492855685 Reorder the terms: 6 + w = -17.492855685 Solving 6 + w = -17.492855685 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + w = -17.492855685 + -6 Combine like terms: 6 + -6 = 0 0 + w = -17.492855685 + -6 w = -17.492855685 + -6 Combine like terms: -17.492855685 + -6 = -23.492855685 w = -23.492855685 Simplifying w = -23.492855685Solution
The solution to the problem is based on the solutions from the subproblems. w = {11.492855685, -23.492855685}
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