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Simplifying -8w2 + -8w + 19 = 0 Reorder the terms: 19 + -8w + -8w2 = 0 Solving 19 + -8w + -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'. -2.375 + w + w2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + w + 2.375 + w2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + w + w2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + w + w2 = 0 + 2.375 w + w2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 w + w2 = 2.375 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + w2 = 2.375 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + w2 = 2.375 + 0.25 Combine like terms: 2.375 + 0.25 = 2.625 1.25 + w2 = 2.625 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 2.625 Calculate the square root of the right side: 1.620185175 Break this problem into two subproblems by setting (w + 0.5) equal to 1.620185175 and -1.620185175.Subproblem 1
w + 0.5 = 1.620185175 Simplifying w + 0.5 = 1.620185175 Reorder the terms: 0.5 + w = 1.620185175 Solving 0.5 + w = 1.620185175 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 1.620185175 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 1.620185175 + -0.5 w = 1.620185175 + -0.5 Combine like terms: 1.620185175 + -0.5 = 1.120185175 w = 1.120185175 Simplifying w = 1.120185175Subproblem 2
w + 0.5 = -1.620185175 Simplifying w + 0.5 = -1.620185175 Reorder the terms: 0.5 + w = -1.620185175 Solving 0.5 + w = -1.620185175 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -1.620185175 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -1.620185175 + -0.5 w = -1.620185175 + -0.5 Combine like terms: -1.620185175 + -0.5 = -2.120185175 w = -2.120185175 Simplifying w = -2.120185175Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.120185175, -2.120185175}
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