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Simplifying x = 12x2 + -64x + 64 Reorder the terms: x = 64 + -64x + 12x2 Solving x = 64 + -64x + 12x2 Solving for variable 'x'. Reorder the terms: -64 + x + 64x + -12x2 = 64 + -64x + 12x2 + -64 + 64x + -12x2 Combine like terms: x + 64x = 65x -64 + 65x + -12x2 = 64 + -64x + 12x2 + -64 + 64x + -12x2 Reorder the terms: -64 + 65x + -12x2 = 64 + -64 + -64x + 64x + 12x2 + -12x2 Combine like terms: 64 + -64 = 0 -64 + 65x + -12x2 = 0 + -64x + 64x + 12x2 + -12x2 -64 + 65x + -12x2 = -64x + 64x + 12x2 + -12x2 Combine like terms: -64x + 64x = 0 -64 + 65x + -12x2 = 0 + 12x2 + -12x2 -64 + 65x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -64 + 65x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 5.333333333 + -5.416666667x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -5.416666667x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -5.416666667x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -5.416666667x + x2 = 0 + -5.333333333 -5.416666667x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -5.416666667x + x2 = -5.333333333 The x term is -5.416666667x. Take half its coefficient (-2.708333334). Square it (7.335069448) and add it to both sides. Add '7.335069448' to each side of the equation. -5.416666667x + 7.335069448 + x2 = -5.333333333 + 7.335069448 Reorder the terms: 7.335069448 + -5.416666667x + x2 = -5.333333333 + 7.335069448 Combine like terms: -5.333333333 + 7.335069448 = 2.001736115 7.335069448 + -5.416666667x + x2 = 2.001736115 Factor a perfect square on the left side: (x + -2.708333334)(x + -2.708333334) = 2.001736115 Calculate the square root of the right side: 1.414827239 Break this problem into two subproblems by setting (x + -2.708333334) equal to 1.414827239 and -1.414827239.Subproblem 1
x + -2.708333334 = 1.414827239 Simplifying x + -2.708333334 = 1.414827239 Reorder the terms: -2.708333334 + x = 1.414827239 Solving -2.708333334 + x = 1.414827239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.708333334' to each side of the equation. -2.708333334 + 2.708333334 + x = 1.414827239 + 2.708333334 Combine like terms: -2.708333334 + 2.708333334 = 0.000000000 0.000000000 + x = 1.414827239 + 2.708333334 x = 1.414827239 + 2.708333334 Combine like terms: 1.414827239 + 2.708333334 = 4.123160573 x = 4.123160573 Simplifying x = 4.123160573Subproblem 2
x + -2.708333334 = -1.414827239 Simplifying x + -2.708333334 = -1.414827239 Reorder the terms: -2.708333334 + x = -1.414827239 Solving -2.708333334 + x = -1.414827239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.708333334' to each side of the equation. -2.708333334 + 2.708333334 + x = -1.414827239 + 2.708333334 Combine like terms: -2.708333334 + 2.708333334 = 0.000000000 0.000000000 + x = -1.414827239 + 2.708333334 x = -1.414827239 + 2.708333334 Combine like terms: -1.414827239 + 2.708333334 = 1.293506095 x = 1.293506095 Simplifying x = 1.293506095Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.123160573, 1.293506095}
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