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Simplifying x2 + 147x + -50 = 0 Reorder the terms: -50 + 147x + x2 = 0 Solving -50 + 147x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 147x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 147x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 147x + x2 = 0 + 50 147x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 147x + x2 = 50 The x term is 147x. Take half its coefficient (73.5). Square it (5402.25) and add it to both sides. Add '5402.25' to each side of the equation. 147x + 5402.25 + x2 = 50 + 5402.25 Reorder the terms: 5402.25 + 147x + x2 = 50 + 5402.25 Combine like terms: 50 + 5402.25 = 5452.25 5402.25 + 147x + x2 = 5452.25 Factor a perfect square on the left side: (x + 73.5)(x + 73.5) = 5452.25 Calculate the square root of the right side: 73.839352652 Break this problem into two subproblems by setting (x + 73.5) equal to 73.839352652 and -73.839352652.Subproblem 1
x + 73.5 = 73.839352652 Simplifying x + 73.5 = 73.839352652 Reorder the terms: 73.5 + x = 73.839352652 Solving 73.5 + x = 73.839352652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-73.5' to each side of the equation. 73.5 + -73.5 + x = 73.839352652 + -73.5 Combine like terms: 73.5 + -73.5 = 0.0 0.0 + x = 73.839352652 + -73.5 x = 73.839352652 + -73.5 Combine like terms: 73.839352652 + -73.5 = 0.339352652 x = 0.339352652 Simplifying x = 0.339352652Subproblem 2
x + 73.5 = -73.839352652 Simplifying x + 73.5 = -73.839352652 Reorder the terms: 73.5 + x = -73.839352652 Solving 73.5 + x = -73.839352652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-73.5' to each side of the equation. 73.5 + -73.5 + x = -73.839352652 + -73.5 Combine like terms: 73.5 + -73.5 = 0.0 0.0 + x = -73.839352652 + -73.5 x = -73.839352652 + -73.5 Combine like terms: -73.839352652 + -73.5 = -147.339352652 x = -147.339352652 Simplifying x = -147.339352652Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.339352652, -147.339352652}
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