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Simplifying 0 = -8w2 + 6w + 13 Reorder the terms: 0 = 13 + 6w + -8w2 Solving 0 = 13 + 6w + -8w2 Solving for variable 'w'. Combine like terms: 0 + -13 = -13 -13 + -6w + 8w2 = 13 + 6w + -8w2 + -13 + -6w + 8w2 Reorder the terms: -13 + -6w + 8w2 = 13 + -13 + 6w + -6w + -8w2 + 8w2 Combine like terms: 13 + -13 = 0 -13 + -6w + 8w2 = 0 + 6w + -6w + -8w2 + 8w2 -13 + -6w + 8w2 = 6w + -6w + -8w2 + 8w2 Combine like terms: 6w + -6w = 0 -13 + -6w + 8w2 = 0 + -8w2 + 8w2 -13 + -6w + 8w2 = -8w2 + 8w2 Combine like terms: -8w2 + 8w2 = 0 -13 + -6w + 8w2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + -0.75w + w2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + -0.75w + 1.625 + w2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + -0.75w + w2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + -0.75w + w2 = 0 + 1.625 -0.75w + w2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 -0.75w + w2 = 1.625 The w term is -0.75w. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75w + 0.140625 + w2 = 1.625 + 0.140625 Reorder the terms: 0.140625 + -0.75w + w2 = 1.625 + 0.140625 Combine like terms: 1.625 + 0.140625 = 1.765625 0.140625 + -0.75w + w2 = 1.765625 Factor a perfect square on the left side: (w + -0.375)(w + -0.375) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (w + -0.375) equal to 1.328768227 and -1.328768227.Subproblem 1
w + -0.375 = 1.328768227 Simplifying w + -0.375 = 1.328768227 Reorder the terms: -0.375 + w = 1.328768227 Solving -0.375 + w = 1.328768227 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + w = 1.328768227 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + w = 1.328768227 + 0.375 w = 1.328768227 + 0.375 Combine like terms: 1.328768227 + 0.375 = 1.703768227 w = 1.703768227 Simplifying w = 1.703768227Subproblem 2
w + -0.375 = -1.328768227 Simplifying w + -0.375 = -1.328768227 Reorder the terms: -0.375 + w = -1.328768227 Solving -0.375 + w = -1.328768227 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + w = -1.328768227 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + w = -1.328768227 + 0.375 w = -1.328768227 + 0.375 Combine like terms: -1.328768227 + 0.375 = -0.953768227 w = -0.953768227 Simplifying w = -0.953768227Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.703768227, -0.953768227}
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