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Simplifying 2w2 + -16w + 30 + -1w2 + -25 = 0 Reorder the terms: 30 + -25 + -16w + 2w2 + -1w2 = 0 Combine like terms: 30 + -25 = 5 5 + -16w + 2w2 + -1w2 = 0 Combine like terms: 2w2 + -1w2 = 1w2 5 + -16w + 1w2 = 0 Solving 5 + -16w + 1w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -16w + -5 + w2 = 0 + -5 Reorder the terms: 5 + -5 + -16w + w2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -16w + w2 = 0 + -5 -16w + w2 = 0 + -5 Combine like terms: 0 + -5 = -5 -16w + w2 = -5 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 = -5 + 64 Reorder the terms: 64 + -16w + w2 = -5 + 64 Combine like terms: -5 + 64 = 59 64 + -16w + w2 = 59 Factor a perfect square on the left side: (w + -8)(w + -8) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (w + -8) equal to 7.681145748 and -7.681145748.Subproblem 1
w + -8 = 7.681145748 Simplifying w + -8 = 7.681145748 Reorder the terms: -8 + w = 7.681145748 Solving -8 + w = 7.681145748 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 = 7.681145748 + 8 Combine like terms: -8 + 8 = 0 0 + w = 7.681145748 + 8 w = 7.681145748 + 8 Combine like terms: 7.681145748 + 8 = 15.681145748 w = 15.681145748 Simplifying w = 15.681145748Subproblem 2
w + -8 = -7.681145748 Simplifying w + -8 = -7.681145748 Reorder the terms: -8 + w = -7.681145748 Solving -8 + w = -7.681145748 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 = -7.681145748 + 8 Combine like terms: -8 + 8 = 0 0 + w = -7.681145748 + 8 w = -7.681145748 + 8 Combine like terms: -7.681145748 + 8 = 0.318854252 w = 0.318854252 Simplifying w = 0.318854252Solution
The solution to the problem is based on the solutions from the subproblems. w = {15.681145748, 0.318854252}
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