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Simplifying 8w2 + 15w + -26 = 0 Reorder the terms: -26 + 15w + 8w2 = 0 Solving -26 + 15w + 8w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.25 + 1.875w + w2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 1.875w + 3.25 + w2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 1.875w + w2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 1.875w + w2 = 0 + 3.25 1.875w + w2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 1.875w + w2 = 3.25 The w term is 1.875w. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875w + 0.87890625 + w2 = 3.25 + 0.87890625 Reorder the terms: 0.87890625 + 1.875w + w2 = 3.25 + 0.87890625 Combine like terms: 3.25 + 0.87890625 = 4.12890625 0.87890625 + 1.875w + w2 = 4.12890625 Factor a perfect square on the left side: (w + 0.9375)(w + 0.9375) = 4.12890625 Calculate the square root of the right side: 2.031971026 Break this problem into two subproblems by setting (w + 0.9375) equal to 2.031971026 and -2.031971026.Subproblem 1
w + 0.9375 = 2.031971026 Simplifying w + 0.9375 = 2.031971026 Reorder the terms: 0.9375 + w = 2.031971026 Solving 0.9375 + w = 2.031971026 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + w = 2.031971026 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + w = 2.031971026 + -0.9375 w = 2.031971026 + -0.9375 Combine like terms: 2.031971026 + -0.9375 = 1.094471026 w = 1.094471026 Simplifying w = 1.094471026Subproblem 2
w + 0.9375 = -2.031971026 Simplifying w + 0.9375 = -2.031971026 Reorder the terms: 0.9375 + w = -2.031971026 Solving 0.9375 + w = -2.031971026 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + w = -2.031971026 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + w = -2.031971026 + -0.9375 w = -2.031971026 + -0.9375 Combine like terms: -2.031971026 + -0.9375 = -2.969471026 w = -2.969471026 Simplifying w = -2.969471026Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.094471026, -2.969471026}
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