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Simplifying 28 = w(w + 2) Reorder the terms: 28 = w(2 + w) 28 = (2 * w + w * w) 28 = (2w + w2) Solving 28 = 2w + w2 Solving for variable 'w'. Reorder the terms: 28 + -2w + -1w2 = 2w + -2w + w2 + -1w2 Combine like terms: 2w + -2w = 0 28 + -2w + -1w2 = 0 + w2 + -1w2 28 + -2w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 28 + -2w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + 2w + w2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 2w + 28 + w2 = 0 + 28 Reorder the terms: -28 + 28 + 2w + w2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 2w + w2 = 0 + 28 2w + w2 = 0 + 28 Combine like terms: 0 + 28 = 28 2w + w2 = 28 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 = 28 + 1 Reorder the terms: 1 + 2w + w2 = 28 + 1 Combine like terms: 28 + 1 = 29 1 + 2w + w2 = 29 Factor a perfect square on the left side: (w + 1)(w + 1) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (w + 1) equal to 5.385164807 and -5.385164807.Subproblem 1
w + 1 = 5.385164807 Simplifying w + 1 = 5.385164807 Reorder the terms: 1 + w = 5.385164807 Solving 1 + w = 5.385164807 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 = 5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + w = 5.385164807 + -1 w = 5.385164807 + -1 Combine like terms: 5.385164807 + -1 = 4.385164807 w = 4.385164807 Simplifying w = 4.385164807Subproblem 2
w + 1 = -5.385164807 Simplifying w + 1 = -5.385164807 Reorder the terms: 1 + w = -5.385164807 Solving 1 + w = -5.385164807 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 = -5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + w = -5.385164807 + -1 w = -5.385164807 + -1 Combine like terms: -5.385164807 + -1 = -6.385164807 w = -6.385164807 Simplifying w = -6.385164807Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.385164807, -6.385164807}
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