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Simplifying w(w + 6) = 12 Reorder the terms: w(6 + w) = 12 (6 * w + w * w) = 12 (6w + w2) = 12 Solving 6w + w2 = 12 Solving for variable 'w'. Reorder the terms: -12 + 6w + w2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 6w + 12 + w2 = 0 + 12 Reorder the terms: -12 + 12 + 6w + w2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 6w + w2 = 0 + 12 6w + w2 = 0 + 12 Combine like terms: 0 + 12 = 12 6w + w2 = 12 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 = 12 + 9 Reorder the terms: 9 + 6w + w2 = 12 + 9 Combine like terms: 12 + 9 = 21 9 + 6w + w2 = 21 Factor a perfect square on the left side: (w + 3)(w + 3) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (w + 3) equal to 4.582575695 and -4.582575695.Subproblem 1
w + 3 = 4.582575695 Simplifying w + 3 = 4.582575695 Reorder the terms: 3 + w = 4.582575695 Solving 3 + w = 4.582575695 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 = 4.582575695 + -3 Combine like terms: 3 + -3 = 0 0 + w = 4.582575695 + -3 w = 4.582575695 + -3 Combine like terms: 4.582575695 + -3 = 1.582575695 w = 1.582575695 Simplifying w = 1.582575695Subproblem 2
w + 3 = -4.582575695 Simplifying w + 3 = -4.582575695 Reorder the terms: 3 + w = -4.582575695 Solving 3 + w = -4.582575695 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 = -4.582575695 + -3 Combine like terms: 3 + -3 = 0 0 + w = -4.582575695 + -3 w = -4.582575695 + -3 Combine like terms: -4.582575695 + -3 = -7.582575695 w = -7.582575695 Simplifying w = -7.582575695Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.582575695, -7.582575695}
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