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Simplifying -1w2 + 16w + 256 = 0 Reorder the terms: 256 + 16w + -1w2 = 0 Solving 256 + 16w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -256 + -16w + w2 = 0 Move the constant term to the right: Add '256' to each side of the equation. -256 + -16w + 256 + w2 = 0 + 256 Reorder the terms: -256 + 256 + -16w + w2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + -16w + w2 = 0 + 256 -16w + w2 = 0 + 256 Combine like terms: 0 + 256 = 256 -16w + w2 = 256 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 = 256 + 64 Reorder the terms: 64 + -16w + w2 = 256 + 64 Combine like terms: 256 + 64 = 320 64 + -16w + w2 = 320 Factor a perfect square on the left side: (w + -8)(w + -8) = 320 Calculate the square root of the right side: 17.88854382 Break this problem into two subproblems by setting (w + -8) equal to 17.88854382 and -17.88854382.Subproblem 1
w + -8 = 17.88854382 Simplifying w + -8 = 17.88854382 Reorder the terms: -8 + w = 17.88854382 Solving -8 + w = 17.88854382 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 = 17.88854382 + 8 Combine like terms: -8 + 8 = 0 0 + w = 17.88854382 + 8 w = 17.88854382 + 8 Combine like terms: 17.88854382 + 8 = 25.88854382 w = 25.88854382 Simplifying w = 25.88854382Subproblem 2
w + -8 = -17.88854382 Simplifying w + -8 = -17.88854382 Reorder the terms: -8 + w = -17.88854382 Solving -8 + w = -17.88854382 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 = -17.88854382 + 8 Combine like terms: -8 + 8 = 0 0 + w = -17.88854382 + 8 w = -17.88854382 + 8 Combine like terms: -17.88854382 + 8 = -9.88854382 w = -9.88854382 Simplifying w = -9.88854382Solution
The solution to the problem is based on the solutions from the subproblems. w = {25.88854382, -9.88854382}
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