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Simplifying x2 + -50x + 100 = 8400 Reorder the terms: 100 + -50x + x2 = 8400 Solving 100 + -50x + x2 = 8400 Solving for variable 'x'. Reorder the terms: 100 + -8400 + -50x + x2 = 8400 + -8400 Combine like terms: 100 + -8400 = -8300 -8300 + -50x + x2 = 8400 + -8400 Combine like terms: 8400 + -8400 = 0 -8300 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8300' to each side of the equation. -8300 + -50x + 8300 + x2 = 0 + 8300 Reorder the terms: -8300 + 8300 + -50x + x2 = 0 + 8300 Combine like terms: -8300 + 8300 = 0 0 + -50x + x2 = 0 + 8300 -50x + x2 = 0 + 8300 Combine like terms: 0 + 8300 = 8300 -50x + x2 = 8300 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 = 8300 + 625 Reorder the terms: 625 + -50x + x2 = 8300 + 625 Combine like terms: 8300 + 625 = 8925 625 + -50x + x2 = 8925 Factor a perfect square on the left side: (x + -25)(x + -25) = 8925 Calculate the square root of the right side: 94.472218138 Break this problem into two subproblems by setting (x + -25) equal to 94.472218138 and -94.472218138.Subproblem 1
x + -25 = 94.472218138 Simplifying x + -25 = 94.472218138 Reorder the terms: -25 + x = 94.472218138 Solving -25 + x = 94.472218138 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 = 94.472218138 + 25 Combine like terms: -25 + 25 = 0 0 + x = 94.472218138 + 25 x = 94.472218138 + 25 Combine like terms: 94.472218138 + 25 = 119.472218138 x = 119.472218138 Simplifying x = 119.472218138Subproblem 2
x + -25 = -94.472218138 Simplifying x + -25 = -94.472218138 Reorder the terms: -25 + x = -94.472218138 Solving -25 + x = -94.472218138 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 = -94.472218138 + 25 Combine like terms: -25 + 25 = 0 0 + x = -94.472218138 + 25 x = -94.472218138 + 25 Combine like terms: -94.472218138 + 25 = -69.472218138 x = -69.472218138 Simplifying x = -69.472218138Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.472218138, -69.472218138}
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