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Simplifying x2 + -46x + -1 = 125 Reorder the terms: -1 + -46x + x2 = 125 Solving -1 + -46x + x2 = 125 Solving for variable 'x'. Reorder the terms: -1 + -125 + -46x + x2 = 125 + -125 Combine like terms: -1 + -125 = -126 -126 + -46x + x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -126 + -46x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + -46x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + -46x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + -46x + x2 = 0 + 126 -46x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 -46x + x2 = 126 The x term is -46x. Take half its coefficient (-23). Square it (529) and add it to both sides. Add '529' to each side of the equation. -46x + 529 + x2 = 126 + 529 Reorder the terms: 529 + -46x + x2 = 126 + 529 Combine like terms: 126 + 529 = 655 529 + -46x + x2 = 655 Factor a perfect square on the left side: (x + -23)(x + -23) = 655 Calculate the square root of the right side: 25.592967784 Break this problem into two subproblems by setting (x + -23) equal to 25.592967784 and -25.592967784.Subproblem 1
x + -23 = 25.592967784 Simplifying x + -23 = 25.592967784 Reorder the terms: -23 + x = 25.592967784 Solving -23 + x = 25.592967784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = 25.592967784 + 23 Combine like terms: -23 + 23 = 0 0 + x = 25.592967784 + 23 x = 25.592967784 + 23 Combine like terms: 25.592967784 + 23 = 48.592967784 x = 48.592967784 Simplifying x = 48.592967784Subproblem 2
x + -23 = -25.592967784 Simplifying x + -23 = -25.592967784 Reorder the terms: -23 + x = -25.592967784 Solving -23 + x = -25.592967784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = -25.592967784 + 23 Combine like terms: -23 + 23 = 0 0 + x = -25.592967784 + 23 x = -25.592967784 + 23 Combine like terms: -25.592967784 + 23 = -2.592967784 x = -2.592967784 Simplifying x = -2.592967784Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.592967784, -2.592967784}
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