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Simplifying x2 + 50x + -3000 = 0 Reorder the terms: -3000 + 50x + x2 = 0 Solving -3000 + 50x + 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 + 50x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 50x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 50x + x2 = 0 + 3000 50x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 50x + x2 = 3000 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 3000 + 625 Reorder the terms: 625 + 50x + x2 = 3000 + 625 Combine like terms: 3000 + 625 = 3625 625 + 50x + x2 = 3625 Factor a perfect square on the left side: (x + 25)(x + 25) = 3625 Calculate the square root of the right side: 60.207972894 Break this problem into two subproblems by setting (x + 25) equal to 60.207972894 and -60.207972894.Subproblem 1
x + 25 = 60.207972894 Simplifying x + 25 = 60.207972894 Reorder the terms: 25 + x = 60.207972894 Solving 25 + x = 60.207972894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 60.207972894 + -25 Combine like terms: 25 + -25 = 0 0 + x = 60.207972894 + -25 x = 60.207972894 + -25 Combine like terms: 60.207972894 + -25 = 35.207972894 x = 35.207972894 Simplifying x = 35.207972894Subproblem 2
x + 25 = -60.207972894 Simplifying x + 25 = -60.207972894 Reorder the terms: 25 + x = -60.207972894 Solving 25 + x = -60.207972894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -60.207972894 + -25 Combine like terms: 25 + -25 = 0 0 + x = -60.207972894 + -25 x = -60.207972894 + -25 Combine like terms: -60.207972894 + -25 = -85.207972894 x = -85.207972894 Simplifying x = -85.207972894Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.207972894, -85.207972894}
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