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Simplifying w2 + 6w + -28 = 0 Reorder the terms: -28 + 6w + w2 = 0 Solving -28 + 6w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 6w + 28 + w2 = 0 + 28 Reorder the terms: -28 + 28 + 6w + w2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 6w + w2 = 0 + 28 6w + w2 = 0 + 28 Combine like terms: 0 + 28 = 28 6w + w2 = 28 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 = 28 + 9 Reorder the terms: 9 + 6w + w2 = 28 + 9 Combine like terms: 28 + 9 = 37 9 + 6w + w2 = 37 Factor a perfect square on the left side: (w + 3)(w + 3) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (w + 3) equal to 6.08276253 and -6.08276253.Subproblem 1
w + 3 = 6.08276253 Simplifying w + 3 = 6.08276253 Reorder the terms: 3 + w = 6.08276253 Solving 3 + w = 6.08276253 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 = 6.08276253 + -3 Combine like terms: 3 + -3 = 0 0 + w = 6.08276253 + -3 w = 6.08276253 + -3 Combine like terms: 6.08276253 + -3 = 3.08276253 w = 3.08276253 Simplifying w = 3.08276253Subproblem 2
w + 3 = -6.08276253 Simplifying w + 3 = -6.08276253 Reorder the terms: 3 + w = -6.08276253 Solving 3 + w = -6.08276253 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 = -6.08276253 + -3 Combine like terms: 3 + -3 = 0 0 + w = -6.08276253 + -3 w = -6.08276253 + -3 Combine like terms: -6.08276253 + -3 = -9.08276253 w = -9.08276253 Simplifying w = -9.08276253Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.08276253, -9.08276253}
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