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Simplifying -97 = -16x2 + 41x Reorder the terms: -97 = 41x + -16x2 Solving -97 = 41x + -16x2 Solving for variable 'x'. Reorder the terms: -97 + -41x + 16x2 = 41x + -41x + -16x2 + 16x2 Combine like terms: 41x + -41x = 0 -97 + -41x + 16x2 = 0 + -16x2 + 16x2 -97 + -41x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -97 + -41x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.0625 + -2.5625x + x2 = 0 Move the constant term to the right: Add '6.0625' to each side of the equation. -6.0625 + -2.5625x + 6.0625 + x2 = 0 + 6.0625 Reorder the terms: -6.0625 + 6.0625 + -2.5625x + x2 = 0 + 6.0625 Combine like terms: -6.0625 + 6.0625 = 0.0000 0.0000 + -2.5625x + x2 = 0 + 6.0625 -2.5625x + x2 = 0 + 6.0625 Combine like terms: 0 + 6.0625 = 6.0625 -2.5625x + x2 = 6.0625 The x term is -2.5625x. Take half its coefficient (-1.28125). Square it (1.641601563) and add it to both sides. Add '1.641601563' to each side of the equation. -2.5625x + 1.641601563 + x2 = 6.0625 + 1.641601563 Reorder the terms: 1.641601563 + -2.5625x + x2 = 6.0625 + 1.641601563 Combine like terms: 6.0625 + 1.641601563 = 7.704101563 1.641601563 + -2.5625x + x2 = 7.704101563 Factor a perfect square on the left side: (x + -1.28125)(x + -1.28125) = 7.704101563 Calculate the square root of the right side: 2.775626337 Break this problem into two subproblems by setting (x + -1.28125) equal to 2.775626337 and -2.775626337.Subproblem 1
x + -1.28125 = 2.775626337 Simplifying x + -1.28125 = 2.775626337 Reorder the terms: -1.28125 + x = 2.775626337 Solving -1.28125 + x = 2.775626337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.28125' to each side of the equation. -1.28125 + 1.28125 + x = 2.775626337 + 1.28125 Combine like terms: -1.28125 + 1.28125 = 0.00000 0.00000 + x = 2.775626337 + 1.28125 x = 2.775626337 + 1.28125 Combine like terms: 2.775626337 + 1.28125 = 4.056876337 x = 4.056876337 Simplifying x = 4.056876337Subproblem 2
x + -1.28125 = -2.775626337 Simplifying x + -1.28125 = -2.775626337 Reorder the terms: -1.28125 + x = -2.775626337 Solving -1.28125 + x = -2.775626337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.28125' to each side of the equation. -1.28125 + 1.28125 + x = -2.775626337 + 1.28125 Combine like terms: -1.28125 + 1.28125 = 0.00000 0.00000 + x = -2.775626337 + 1.28125 x = -2.775626337 + 1.28125 Combine like terms: -2.775626337 + 1.28125 = -1.494376337 x = -1.494376337 Simplifying x = -1.494376337Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.056876337, -1.494376337}
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