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Simplifying 14x2 + 46x + -71 = 0 Reorder the terms: -71 + 46x + 14x2 = 0 Solving -71 + 46x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -5.071428571 + 3.285714286x + x2 = 0 Move the constant term to the right: Add '5.071428571' to each side of the equation. -5.071428571 + 3.285714286x + 5.071428571 + x2 = 0 + 5.071428571 Reorder the terms: -5.071428571 + 5.071428571 + 3.285714286x + x2 = 0 + 5.071428571 Combine like terms: -5.071428571 + 5.071428571 = 0.000000000 0.000000000 + 3.285714286x + x2 = 0 + 5.071428571 3.285714286x + x2 = 0 + 5.071428571 Combine like terms: 0 + 5.071428571 = 5.071428571 3.285714286x + x2 = 5.071428571 The x term is 3.285714286x. Take half its coefficient (1.642857143). Square it (2.698979592) and add it to both sides. Add '2.698979592' to each side of the equation. 3.285714286x + 2.698979592 + x2 = 5.071428571 + 2.698979592 Reorder the terms: 2.698979592 + 3.285714286x + x2 = 5.071428571 + 2.698979592 Combine like terms: 5.071428571 + 2.698979592 = 7.770408163 2.698979592 + 3.285714286x + x2 = 7.770408163 Factor a perfect square on the left side: (x + 1.642857143)(x + 1.642857143) = 7.770408163 Calculate the square root of the right side: 2.787545186 Break this problem into two subproblems by setting (x + 1.642857143) equal to 2.787545186 and -2.787545186.Subproblem 1
x + 1.642857143 = 2.787545186 Simplifying x + 1.642857143 = 2.787545186 Reorder the terms: 1.642857143 + x = 2.787545186 Solving 1.642857143 + x = 2.787545186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x = 2.787545186 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = 2.787545186 + -1.642857143 x = 2.787545186 + -1.642857143 Combine like terms: 2.787545186 + -1.642857143 = 1.144688043 x = 1.144688043 Simplifying x = 1.144688043Subproblem 2
x + 1.642857143 = -2.787545186 Simplifying x + 1.642857143 = -2.787545186 Reorder the terms: 1.642857143 + x = -2.787545186 Solving 1.642857143 + x = -2.787545186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x = -2.787545186 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = -2.787545186 + -1.642857143 x = -2.787545186 + -1.642857143 Combine like terms: -2.787545186 + -1.642857143 = -4.430402329 x = -4.430402329 Simplifying x = -4.430402329Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.144688043, -4.430402329}
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