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Simplifying w2 + 2w = 19 Reorder the terms: 2w + w2 = 19 Solving 2w + w2 = 19 Solving for variable 'w'. Reorder the terms: -19 + 2w + w2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 2w + 19 + w2 = 0 + 19 Reorder the terms: -19 + 19 + 2w + w2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 2w + w2 = 0 + 19 2w + w2 = 0 + 19 Combine like terms: 0 + 19 = 19 2w + w2 = 19 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 = 19 + 1 Reorder the terms: 1 + 2w + w2 = 19 + 1 Combine like terms: 19 + 1 = 20 1 + 2w + w2 = 20 Factor a perfect square on the left side: (w + 1)(w + 1) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (w + 1) equal to 4.472135955 and -4.472135955.Subproblem 1
w + 1 = 4.472135955 Simplifying w + 1 = 4.472135955 Reorder the terms: 1 + w = 4.472135955 Solving 1 + w = 4.472135955 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 = 4.472135955 + -1 Combine like terms: 1 + -1 = 0 0 + w = 4.472135955 + -1 w = 4.472135955 + -1 Combine like terms: 4.472135955 + -1 = 3.472135955 w = 3.472135955 Simplifying w = 3.472135955Subproblem 2
w + 1 = -4.472135955 Simplifying w + 1 = -4.472135955 Reorder the terms: 1 + w = -4.472135955 Solving 1 + w = -4.472135955 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 = -4.472135955 + -1 Combine like terms: 1 + -1 = 0 0 + w = -4.472135955 + -1 w = -4.472135955 + -1 Combine like terms: -4.472135955 + -1 = -5.472135955 w = -5.472135955 Simplifying w = -5.472135955Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.472135955, -5.472135955}
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