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Simplifying w(w + 2) = 7 Reorder the terms: w(2 + w) = 7 (2 * w + w * w) = 7 (2w + w2) = 7 Solving 2w + w2 = 7 Solving for variable 'w'. Reorder the terms: -7 + 2w + w2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 2w + 7 + w2 = 0 + 7 Reorder the terms: -7 + 7 + 2w + w2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2w + w2 = 0 + 7 2w + w2 = 0 + 7 Combine like terms: 0 + 7 = 7 2w + w2 = 7 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 = 7 + 1 Reorder the terms: 1 + 2w + w2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + 2w + w2 = 8 Factor a perfect square on the left side: (w + 1)(w + 1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (w + 1) equal to 2.828427125 and -2.828427125.Subproblem 1
w + 1 = 2.828427125 Simplifying w + 1 = 2.828427125 Reorder the terms: 1 + w = 2.828427125 Solving 1 + w = 2.828427125 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 = 2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + w = 2.828427125 + -1 w = 2.828427125 + -1 Combine like terms: 2.828427125 + -1 = 1.828427125 w = 1.828427125 Simplifying w = 1.828427125Subproblem 2
w + 1 = -2.828427125 Simplifying w + 1 = -2.828427125 Reorder the terms: 1 + w = -2.828427125 Solving 1 + w = -2.828427125 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 = -2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + w = -2.828427125 + -1 w = -2.828427125 + -1 Combine like terms: -2.828427125 + -1 = -3.828427125 w = -3.828427125 Simplifying w = -3.828427125Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.828427125, -3.828427125}
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