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Simplifying x * x + 100x + -3000 = 0 Multiply x * x x2 + 100x + -3000 = 0 Reorder the terms: -3000 + 100x + x2 = 0 Solving -3000 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3000' to each side of the equation. -3000 + 100x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 100x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 100x + x2 = 0 + 3000 100x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 100x + x2 = 3000 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 3000 + 2500 Reorder the terms: 2500 + 100x + x2 = 3000 + 2500 Combine like terms: 3000 + 2500 = 5500 2500 + 100x + x2 = 5500 Factor a perfect square on the left side: (x + 50)(x + 50) = 5500 Calculate the square root of the right side: 74.161984871 Break this problem into two subproblems by setting (x + 50) equal to 74.161984871 and -74.161984871.Subproblem 1
x + 50 = 74.161984871 Simplifying x + 50 = 74.161984871 Reorder the terms: 50 + x = 74.161984871 Solving 50 + x = 74.161984871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 74.161984871 + -50 Combine like terms: 50 + -50 = 0 0 + x = 74.161984871 + -50 x = 74.161984871 + -50 Combine like terms: 74.161984871 + -50 = 24.161984871 x = 24.161984871 Simplifying x = 24.161984871Subproblem 2
x + 50 = -74.161984871 Simplifying x + 50 = -74.161984871 Reorder the terms: 50 + x = -74.161984871 Solving 50 + x = -74.161984871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -74.161984871 + -50 Combine like terms: 50 + -50 = 0 0 + x = -74.161984871 + -50 x = -74.161984871 + -50 Combine like terms: -74.161984871 + -50 = -124.161984871 x = -124.161984871 Simplifying x = -124.161984871Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.161984871, -124.161984871}
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