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Simplifying 12x2 + -128x + 256 = x Reorder the terms: 256 + -128x + 12x2 = x Solving 256 + -128x + 12x2 = x Solving for variable 'x'. Reorder the terms: 256 + -128x + -1x + 12x2 = x + -1x Combine like terms: -128x + -1x = -129x 256 + -129x + 12x2 = x + -1x Combine like terms: x + -1x = 0 256 + -129x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 21.33333333 + -10.75x + x2 = 0 Move the constant term to the right: Add '-21.33333333' to each side of the equation. 21.33333333 + -10.75x + -21.33333333 + x2 = 0 + -21.33333333 Reorder the terms: 21.33333333 + -21.33333333 + -10.75x + x2 = 0 + -21.33333333 Combine like terms: 21.33333333 + -21.33333333 = 0.00000000 0.00000000 + -10.75x + x2 = 0 + -21.33333333 -10.75x + x2 = 0 + -21.33333333 Combine like terms: 0 + -21.33333333 = -21.33333333 -10.75x + x2 = -21.33333333 The x term is -10.75x. Take half its coefficient (-5.375). Square it (28.890625) and add it to both sides. Add '28.890625' to each side of the equation. -10.75x + 28.890625 + x2 = -21.33333333 + 28.890625 Reorder the terms: 28.890625 + -10.75x + x2 = -21.33333333 + 28.890625 Combine like terms: -21.33333333 + 28.890625 = 7.55729167 28.890625 + -10.75x + x2 = 7.55729167 Factor a perfect square on the left side: (x + -5.375)(x + -5.375) = 7.55729167 Calculate the square root of the right side: 2.749052868 Break this problem into two subproblems by setting (x + -5.375) equal to 2.749052868 and -2.749052868.Subproblem 1
x + -5.375 = 2.749052868 Simplifying x + -5.375 = 2.749052868 Reorder the terms: -5.375 + x = 2.749052868 Solving -5.375 + x = 2.749052868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.375' to each side of the equation. -5.375 + 5.375 + x = 2.749052868 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + x = 2.749052868 + 5.375 x = 2.749052868 + 5.375 Combine like terms: 2.749052868 + 5.375 = 8.124052868 x = 8.124052868 Simplifying x = 8.124052868Subproblem 2
x + -5.375 = -2.749052868 Simplifying x + -5.375 = -2.749052868 Reorder the terms: -5.375 + x = -2.749052868 Solving -5.375 + x = -2.749052868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.375' to each side of the equation. -5.375 + 5.375 + x = -2.749052868 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + x = -2.749052868 + 5.375 x = -2.749052868 + 5.375 Combine like terms: -2.749052868 + 5.375 = 2.625947132 x = 2.625947132 Simplifying x = 2.625947132Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.124052868, 2.625947132}
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