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Simplifying 14x2 = 46x + -1 Reorder the terms: 14x2 = -1 + 46x Solving 14x2 = -1 + 46x Solving for variable 'x'. Reorder the terms: 1 + -46x + 14x2 = -1 + 46x + 1 + -46x Reorder the terms: 1 + -46x + 14x2 = -1 + 1 + 46x + -46x Combine like terms: -1 + 1 = 0 1 + -46x + 14x2 = 0 + 46x + -46x 1 + -46x + 14x2 = 46x + -46x Combine like terms: 46x + -46x = 0 1 + -46x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.07142857143 + -3.285714286x + x2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + -3.285714286x + -0.07142857143 + x2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + -3.285714286x + x2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + -3.285714286x + x2 = 0 + -0.07142857143 -3.285714286x + x2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 -3.285714286x + x2 = -0.07142857143 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 = -0.07142857143 + 2.698979592 Reorder the terms: 2.698979592 + -3.285714286x + x2 = -0.07142857143 + 2.698979592 Combine like terms: -0.07142857143 + 2.698979592 = 2.62755102057 2.698979592 + -3.285714286x + x2 = 2.62755102057 Factor a perfect square on the left side: (x + -1.642857143)(x + -1.642857143) = 2.62755102057 Calculate the square root of the right side: 1.620972245 Break this problem into two subproblems by setting (x + -1.642857143) equal to 1.620972245 and -1.620972245.Subproblem 1
x + -1.642857143 = 1.620972245 Simplifying x + -1.642857143 = 1.620972245 Reorder the terms: -1.642857143 + x = 1.620972245 Solving -1.642857143 + x = 1.620972245 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 = 1.620972245 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = 1.620972245 + 1.642857143 x = 1.620972245 + 1.642857143 Combine like terms: 1.620972245 + 1.642857143 = 3.263829388 x = 3.263829388 Simplifying x = 3.263829388Subproblem 2
x + -1.642857143 = -1.620972245 Simplifying x + -1.642857143 = -1.620972245 Reorder the terms: -1.642857143 + x = -1.620972245 Solving -1.642857143 + x = -1.620972245 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 = -1.620972245 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = -1.620972245 + 1.642857143 x = -1.620972245 + 1.642857143 Combine like terms: -1.620972245 + 1.642857143 = 0.021884898 x = 0.021884898 Simplifying x = 0.021884898Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.263829388, 0.021884898}
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