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Simplifying w2 + -2w + -8 = 8 Reorder the terms: -8 + -2w + w2 = 8 Solving -8 + -2w + w2 = 8 Solving for variable 'w'. Reorder the terms: -8 + -8 + -2w + w2 = 8 + -8 Combine like terms: -8 + -8 = -16 -16 + -2w + w2 = 8 + -8 Combine like terms: 8 + -8 = 0 -16 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -2w + 16 + w2 = 0 + 16 Reorder the terms: -16 + 16 + -2w + w2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -2w + w2 = 0 + 16 -2w + w2 = 0 + 16 Combine like terms: 0 + 16 = 16 -2w + w2 = 16 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 = 16 + 1 Reorder the terms: 1 + -2w + w2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + -2w + w2 = 17 Factor a perfect square on the left side: (w + -1)(w + -1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (w + -1) equal to 4.123105626 and -4.123105626.Subproblem 1
w + -1 = 4.123105626 Simplifying w + -1 = 4.123105626 Reorder the terms: -1 + w = 4.123105626 Solving -1 + w = 4.123105626 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 = 4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + w = 4.123105626 + 1 w = 4.123105626 + 1 Combine like terms: 4.123105626 + 1 = 5.123105626 w = 5.123105626 Simplifying w = 5.123105626Subproblem 2
w + -1 = -4.123105626 Simplifying w + -1 = -4.123105626 Reorder the terms: -1 + w = -4.123105626 Solving -1 + w = -4.123105626 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 = -4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + w = -4.123105626 + 1 w = -4.123105626 + 1 Combine like terms: -4.123105626 + 1 = -3.123105626 w = -3.123105626 Simplifying w = -3.123105626Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.123105626, -3.123105626}
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