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Simplifying x2 + 50x + -375 = 0 Reorder the terms: -375 + 50x + x2 = 0 Solving -375 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '375' to each side of the equation. -375 + 50x + 375 + x2 = 0 + 375 Reorder the terms: -375 + 375 + 50x + x2 = 0 + 375 Combine like terms: -375 + 375 = 0 0 + 50x + x2 = 0 + 375 50x + x2 = 0 + 375 Combine like terms: 0 + 375 = 375 50x + x2 = 375 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 = 375 + 625 Reorder the terms: 625 + 50x + x2 = 375 + 625 Combine like terms: 375 + 625 = 1000 625 + 50x + x2 = 1000 Factor a perfect square on the left side: (x + 25)(x + 25) = 1000 Calculate the square root of the right side: 31.622776602 Break this problem into two subproblems by setting (x + 25) equal to 31.622776602 and -31.622776602.Subproblem 1
x + 25 = 31.622776602 Simplifying x + 25 = 31.622776602 Reorder the terms: 25 + x = 31.622776602 Solving 25 + x = 31.622776602 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 = 31.622776602 + -25 Combine like terms: 25 + -25 = 0 0 + x = 31.622776602 + -25 x = 31.622776602 + -25 Combine like terms: 31.622776602 + -25 = 6.622776602 x = 6.622776602 Simplifying x = 6.622776602Subproblem 2
x + 25 = -31.622776602 Simplifying x + 25 = -31.622776602 Reorder the terms: 25 + x = -31.622776602 Solving 25 + x = -31.622776602 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 = -31.622776602 + -25 Combine like terms: 25 + -25 = 0 0 + x = -31.622776602 + -25 x = -31.622776602 + -25 Combine like terms: -31.622776602 + -25 = -56.622776602 x = -56.622776602 Simplifying x = -56.622776602Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.622776602, -56.622776602}
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