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Simplifying (w)(w + 2) = 40 Reorder the terms: w(2 + w) = 40 (2 * w + w * w) = 40 (2w + w2) = 40 Solving 2w + w2 = 40 Solving for variable 'w'. Reorder the terms: -40 + 2w + w2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 2w + 40 + w2 = 0 + 40 Reorder the terms: -40 + 40 + 2w + w2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 2w + w2 = 0 + 40 2w + w2 = 0 + 40 Combine like terms: 0 + 40 = 40 2w + w2 = 40 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 = 40 + 1 Reorder the terms: 1 + 2w + w2 = 40 + 1 Combine like terms: 40 + 1 = 41 1 + 2w + w2 = 41 Factor a perfect square on the left side: (w + 1)(w + 1) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (w + 1) equal to 6.403124237 and -6.403124237.Subproblem 1
w + 1 = 6.403124237 Simplifying w + 1 = 6.403124237 Reorder the terms: 1 + w = 6.403124237 Solving 1 + w = 6.403124237 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 = 6.403124237 + -1 Combine like terms: 1 + -1 = 0 0 + w = 6.403124237 + -1 w = 6.403124237 + -1 Combine like terms: 6.403124237 + -1 = 5.403124237 w = 5.403124237 Simplifying w = 5.403124237Subproblem 2
w + 1 = -6.403124237 Simplifying w + 1 = -6.403124237 Reorder the terms: 1 + w = -6.403124237 Solving 1 + w = -6.403124237 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 = -6.403124237 + -1 Combine like terms: 1 + -1 = 0 0 + w = -6.403124237 + -1 w = -6.403124237 + -1 Combine like terms: -6.403124237 + -1 = -7.403124237 w = -7.403124237 Simplifying w = -7.403124237Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.403124237, -7.403124237}
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