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Simplifying 7x2 + -24x + -125 = 0 Reorder the terms: -125 + -24x + 7x2 = 0 Solving -125 + -24x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -17.85714286 + -3.428571429x + x2 = 0 Move the constant term to the right: Add '17.85714286' to each side of the equation. -17.85714286 + -3.428571429x + 17.85714286 + x2 = 0 + 17.85714286 Reorder the terms: -17.85714286 + 17.85714286 + -3.428571429x + x2 = 0 + 17.85714286 Combine like terms: -17.85714286 + 17.85714286 = 0.00000000 0.00000000 + -3.428571429x + x2 = 0 + 17.85714286 -3.428571429x + x2 = 0 + 17.85714286 Combine like terms: 0 + 17.85714286 = 17.85714286 -3.428571429x + x2 = 17.85714286 The x term is -3.428571429x. Take half its coefficient (-1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. -3.428571429x + 2.938775513 + x2 = 17.85714286 + 2.938775513 Reorder the terms: 2.938775513 + -3.428571429x + x2 = 17.85714286 + 2.938775513 Combine like terms: 17.85714286 + 2.938775513 = 20.795918373 2.938775513 + -3.428571429x + x2 = 20.795918373 Factor a perfect square on the left side: (x + -1.714285715)(x + -1.714285715) = 20.795918373 Calculate the square root of the right side: 4.5602542 Break this problem into two subproblems by setting (x + -1.714285715) equal to 4.5602542 and -4.5602542.Subproblem 1
x + -1.714285715 = 4.5602542 Simplifying x + -1.714285715 = 4.5602542 Reorder the terms: -1.714285715 + x = 4.5602542 Solving -1.714285715 + x = 4.5602542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + x = 4.5602542 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + x = 4.5602542 + 1.714285715 x = 4.5602542 + 1.714285715 Combine like terms: 4.5602542 + 1.714285715 = 6.274539915 x = 6.274539915 Simplifying x = 6.274539915Subproblem 2
x + -1.714285715 = -4.5602542 Simplifying x + -1.714285715 = -4.5602542 Reorder the terms: -1.714285715 + x = -4.5602542 Solving -1.714285715 + x = -4.5602542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + x = -4.5602542 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + x = -4.5602542 + 1.714285715 x = -4.5602542 + 1.714285715 Combine like terms: -4.5602542 + 1.714285715 = -2.845968485 x = -2.845968485 Simplifying x = -2.845968485Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.274539915, -2.845968485}
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