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Simplifying 6w = w * w + 2 Multiply w * w 6w = w2 + 2 Reorder the terms: 6w = 2 + w2 Solving 6w = 2 + w2 Solving for variable 'w'. Reorder the terms: -2 + 6w + -1w2 = 2 + w2 + -2 + -1w2 Reorder the terms: -2 + 6w + -1w2 = 2 + -2 + w2 + -1w2 Combine like terms: 2 + -2 = 0 -2 + 6w + -1w2 = 0 + w2 + -1w2 -2 + 6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -2 + 6w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -6w + w2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + -6w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6w + w2 = 0 + -2 -6w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6w + w2 = -2 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 = -2 + 9 Reorder the terms: 9 + -6w + w2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6w + w2 = 7 Factor a perfect square on the left side: (w + -3)(w + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (w + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
w + -3 = 2.645751311 Simplifying w + -3 = 2.645751311 Reorder the terms: -3 + w = 2.645751311 Solving -3 + w = 2.645751311 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 = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + w = 2.645751311 + 3 w = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 w = 5.645751311 Simplifying w = 5.645751311Subproblem 2
w + -3 = -2.645751311 Simplifying w + -3 = -2.645751311 Reorder the terms: -3 + w = -2.645751311 Solving -3 + w = -2.645751311 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 = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + w = -2.645751311 + 3 w = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 w = 0.354248689 Simplifying w = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.645751311, 0.354248689}
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