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Simplifying w2 + -6w = 9 Reorder the terms: -6w + w2 = 9 Solving -6w + w2 = 9 Solving for variable 'w'. Reorder the terms: -9 + -6w + w2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6w + 9 + w2 = 0 + 9 Reorder the terms: -9 + 9 + -6w + w2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6w + w2 = 0 + 9 -6w + w2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6w + w2 = 9 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 = 9 + 9 Reorder the terms: 9 + -6w + w2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6w + w2 = 18 Factor a perfect square on the left side: (w + -3)(w + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (w + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
w + -3 = 4.242640687 Simplifying w + -3 = 4.242640687 Reorder the terms: -3 + w = 4.242640687 Solving -3 + w = 4.242640687 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 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + w = 4.242640687 + 3 w = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 w = 7.242640687 Simplifying w = 7.242640687Subproblem 2
w + -3 = -4.242640687 Simplifying w + -3 = -4.242640687 Reorder the terms: -3 + w = -4.242640687 Solving -3 + w = -4.242640687 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 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + w = -4.242640687 + 3 w = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 w = -1.242640687 Simplifying w = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.242640687, -1.242640687}
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