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Simplifying w2 + 3w + -91 = 0 Reorder the terms: -91 + 3w + w2 = 0 Solving -91 + 3w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + 3w + 91 + w2 = 0 + 91 Reorder the terms: -91 + 91 + 3w + w2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 3w + w2 = 0 + 91 3w + w2 = 0 + 91 Combine like terms: 0 + 91 = 91 3w + w2 = 91 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 91 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 91 + 2.25 Combine like terms: 91 + 2.25 = 93.25 2.25 + 3w + w2 = 93.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 93.25 Calculate the square root of the right side: 9.656603958 Break this problem into two subproblems by setting (w + 1.5) equal to 9.656603958 and -9.656603958.Subproblem 1
w + 1.5 = 9.656603958 Simplifying w + 1.5 = 9.656603958 Reorder the terms: 1.5 + w = 9.656603958 Solving 1.5 + w = 9.656603958 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 9.656603958 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 9.656603958 + -1.5 w = 9.656603958 + -1.5 Combine like terms: 9.656603958 + -1.5 = 8.156603958 w = 8.156603958 Simplifying w = 8.156603958Subproblem 2
w + 1.5 = -9.656603958 Simplifying w + 1.5 = -9.656603958 Reorder the terms: 1.5 + w = -9.656603958 Solving 1.5 + w = -9.656603958 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -9.656603958 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -9.656603958 + -1.5 w = -9.656603958 + -1.5 Combine like terms: -9.656603958 + -1.5 = -11.156603958 w = -11.156603958 Simplifying w = -11.156603958Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.156603958, -11.156603958}
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