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Simplifying w2 + 3w + -48 = 0 Reorder the terms: -48 + 3w + w2 = 0 Solving -48 + 3w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 3w + 48 + w2 = 0 + 48 Reorder the terms: -48 + 48 + 3w + w2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 3w + w2 = 0 + 48 3w + w2 = 0 + 48 Combine like terms: 0 + 48 = 48 3w + w2 = 48 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 = 48 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 48 + 2.25 Combine like terms: 48 + 2.25 = 50.25 2.25 + 3w + w2 = 50.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (w + 1.5) equal to 7.088723439 and -7.088723439.Subproblem 1
w + 1.5 = 7.088723439 Simplifying w + 1.5 = 7.088723439 Reorder the terms: 1.5 + w = 7.088723439 Solving 1.5 + w = 7.088723439 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 = 7.088723439 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 7.088723439 + -1.5 w = 7.088723439 + -1.5 Combine like terms: 7.088723439 + -1.5 = 5.588723439 w = 5.588723439 Simplifying w = 5.588723439Subproblem 2
w + 1.5 = -7.088723439 Simplifying w + 1.5 = -7.088723439 Reorder the terms: 1.5 + w = -7.088723439 Solving 1.5 + w = -7.088723439 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 = -7.088723439 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -7.088723439 + -1.5 w = -7.088723439 + -1.5 Combine like terms: -7.088723439 + -1.5 = -8.588723439 w = -8.588723439 Simplifying w = -8.588723439Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.588723439, -8.588723439}
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