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Simplifying -4w2 + -64w = -12 Reorder the terms: -64w + -4w2 = -12 Solving -64w + -4w2 = -12 Solving for variable 'w'. Reorder the terms: 12 + -64w + -4w2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -64w + -4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -16w + -1w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -16w + -1w2)' equal to zero and attempt to solve: Simplifying 3 + -16w + -1w2 = 0 Solving 3 + -16w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 16w + w2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 16w + 3 + w2 = 0 + 3 Reorder the terms: -3 + 3 + 16w + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 16w + w2 = 0 + 3 16w + w2 = 0 + 3 Combine like terms: 0 + 3 = 3 16w + w2 = 3 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 = 3 + 64 Reorder the terms: 64 + 16w + w2 = 3 + 64 Combine like terms: 3 + 64 = 67 64 + 16w + w2 = 67 Factor a perfect square on the left side: (w + 8)(w + 8) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (w + 8) equal to 8.185352772 and -8.185352772.Subproblem 1
w + 8 = 8.185352772 Simplifying w + 8 = 8.185352772 Reorder the terms: 8 + w = 8.185352772 Solving 8 + w = 8.185352772 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 = 8.185352772 + -8 Combine like terms: 8 + -8 = 0 0 + w = 8.185352772 + -8 w = 8.185352772 + -8 Combine like terms: 8.185352772 + -8 = 0.185352772 w = 0.185352772 Simplifying w = 0.185352772Subproblem 2
w + 8 = -8.185352772 Simplifying w + 8 = -8.185352772 Reorder the terms: 8 + w = -8.185352772 Solving 8 + w = -8.185352772 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 = -8.185352772 + -8 Combine like terms: 8 + -8 = 0 0 + w = -8.185352772 + -8 w = -8.185352772 + -8 Combine like terms: -8.185352772 + -8 = -16.185352772 w = -16.185352772 Simplifying w = -16.185352772Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.185352772, -16.185352772}Solution
w = {0.185352772, -16.185352772}
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