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Simplifying w2 + 16w + -8 = 0 Reorder the terms: -8 + 16w + w2 = 0 Solving -8 + 16w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 16w + 8 + w2 = 0 + 8 Reorder the terms: -8 + 8 + 16w + w2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 16w + w2 = 0 + 8 16w + w2 = 0 + 8 Combine like terms: 0 + 8 = 8 16w + w2 = 8 The w term is 16w. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16w + 64 + w2 = 8 + 64 Reorder the terms: 64 + 16w + w2 = 8 + 64 Combine like terms: 8 + 64 = 72 64 + 16w + w2 = 72 Factor a perfect square on the left side: (w + 8)(w + 8) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (w + 8) equal to 8.485281374 and -8.485281374.Subproblem 1
w + 8 = 8.485281374 Simplifying w + 8 = 8.485281374 Reorder the terms: 8 + w = 8.485281374 Solving 8 + w = 8.485281374 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = 8.485281374 + -8 Combine like terms: 8 + -8 = 0 0 + w = 8.485281374 + -8 w = 8.485281374 + -8 Combine like terms: 8.485281374 + -8 = 0.485281374 w = 0.485281374 Simplifying w = 0.485281374Subproblem 2
w + 8 = -8.485281374 Simplifying w + 8 = -8.485281374 Reorder the terms: 8 + w = -8.485281374 Solving 8 + w = -8.485281374 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = -8.485281374 + -8 Combine like terms: 8 + -8 = 0 0 + w = -8.485281374 + -8 w = -8.485281374 + -8 Combine like terms: -8.485281374 + -8 = -16.485281374 w = -16.485281374 Simplifying w = -16.485281374Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.485281374, -16.485281374}
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