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Simplifying x2 + 6x2 + -16x + -96 = 0 Reorder the terms: -96 + -16x + x2 + 6x2 = 0 Combine like terms: x2 + 6x2 = 7x2 -96 + -16x + 7x2 = 0 Solving -96 + -16x + 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'. -13.71428571 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '13.71428571' to each side of the equation. -13.71428571 + -2.285714286x + 13.71428571 + x2 = 0 + 13.71428571 Reorder the terms: -13.71428571 + 13.71428571 + -2.285714286x + x2 = 0 + 13.71428571 Combine like terms: -13.71428571 + 13.71428571 = 0.00000000 0.00000000 + -2.285714286x + x2 = 0 + 13.71428571 -2.285714286x + x2 = 0 + 13.71428571 Combine like terms: 0 + 13.71428571 = 13.71428571 -2.285714286x + x2 = 13.71428571 The x term is -2.285714286x. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286x + 1.306122449 + x2 = 13.71428571 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = 13.71428571 + 1.306122449 Combine like terms: 13.71428571 + 1.306122449 = 15.020408159 1.306122449 + -2.285714286x + x2 = 15.020408159 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 15.020408159 Calculate the square root of the right side: 3.875617133 Break this problem into two subproblems by setting (x + -1.142857143) equal to 3.875617133 and -3.875617133.Subproblem 1
x + -1.142857143 = 3.875617133 Simplifying x + -1.142857143 = 3.875617133 Reorder the terms: -1.142857143 + x = 3.875617133 Solving -1.142857143 + x = 3.875617133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = 3.875617133 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 3.875617133 + 1.142857143 x = 3.875617133 + 1.142857143 Combine like terms: 3.875617133 + 1.142857143 = 5.018474276 x = 5.018474276 Simplifying x = 5.018474276Subproblem 2
x + -1.142857143 = -3.875617133 Simplifying x + -1.142857143 = -3.875617133 Reorder the terms: -1.142857143 + x = -3.875617133 Solving -1.142857143 + x = -3.875617133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = -3.875617133 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -3.875617133 + 1.142857143 x = -3.875617133 + 1.142857143 Combine like terms: -3.875617133 + 1.142857143 = -2.73275999 x = -2.73275999 Simplifying x = -2.73275999Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.018474276, -2.73275999}
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