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Simplifying w(w + -2) = 45 Reorder the terms: w(-2 + w) = 45 (-2 * w + w * w) = 45 (-2w + w2) = 45 Solving -2w + w2 = 45 Solving for variable 'w'. Reorder the terms: -45 + -2w + w2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -2w + 45 + w2 = 0 + 45 Reorder the terms: -45 + 45 + -2w + w2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -2w + w2 = 0 + 45 -2w + w2 = 0 + 45 Combine like terms: 0 + 45 = 45 -2w + w2 = 45 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 45 + 1 Reorder the terms: 1 + -2w + w2 = 45 + 1 Combine like terms: 45 + 1 = 46 1 + -2w + w2 = 46 Factor a perfect square on the left side: (w + -1)(w + -1) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (w + -1) equal to 6.782329983 and -6.782329983.Subproblem 1
w + -1 = 6.782329983 Simplifying w + -1 = 6.782329983 Reorder the terms: -1 + w = 6.782329983 Solving -1 + w = 6.782329983 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 6.782329983 + 1 Combine like terms: -1 + 1 = 0 0 + w = 6.782329983 + 1 w = 6.782329983 + 1 Combine like terms: 6.782329983 + 1 = 7.782329983 w = 7.782329983 Simplifying w = 7.782329983Subproblem 2
w + -1 = -6.782329983 Simplifying w + -1 = -6.782329983 Reorder the terms: -1 + w = -6.782329983 Solving -1 + w = -6.782329983 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -6.782329983 + 1 Combine like terms: -1 + 1 = 0 0 + w = -6.782329983 + 1 w = -6.782329983 + 1 Combine like terms: -6.782329983 + 1 = -5.782329983 w = -5.782329983 Simplifying w = -5.782329983Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.782329983, -5.782329983}
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