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Simplifying 14x2 + 53x = 14 Reorder the terms: 53x + 14x2 = 14 Solving 53x + 14x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 53x + 14x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 53x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1 + 3.785714286x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 3.785714286x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 3.785714286x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3.785714286x + x2 = 0 + 1 3.785714286x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 3.785714286x + x2 = 1 The x term is 3.785714286x. Take half its coefficient (1.892857143). Square it (3.582908164) and add it to both sides. Add '3.582908164' to each side of the equation. 3.785714286x + 3.582908164 + x2 = 1 + 3.582908164 Reorder the terms: 3.582908164 + 3.785714286x + x2 = 1 + 3.582908164 Combine like terms: 1 + 3.582908164 = 4.582908164 3.582908164 + 3.785714286x + x2 = 4.582908164 Factor a perfect square on the left side: (x + 1.892857143)(x + 1.892857143) = 4.582908164 Calculate the square root of the right side: 2.140772796 Break this problem into two subproblems by setting (x + 1.892857143) equal to 2.140772796 and -2.140772796.Subproblem 1
x + 1.892857143 = 2.140772796 Simplifying x + 1.892857143 = 2.140772796 Reorder the terms: 1.892857143 + x = 2.140772796 Solving 1.892857143 + x = 2.140772796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.892857143' to each side of the equation. 1.892857143 + -1.892857143 + x = 2.140772796 + -1.892857143 Combine like terms: 1.892857143 + -1.892857143 = 0.000000000 0.000000000 + x = 2.140772796 + -1.892857143 x = 2.140772796 + -1.892857143 Combine like terms: 2.140772796 + -1.892857143 = 0.247915653 x = 0.247915653 Simplifying x = 0.247915653Subproblem 2
x + 1.892857143 = -2.140772796 Simplifying x + 1.892857143 = -2.140772796 Reorder the terms: 1.892857143 + x = -2.140772796 Solving 1.892857143 + x = -2.140772796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.892857143' to each side of the equation. 1.892857143 + -1.892857143 + x = -2.140772796 + -1.892857143 Combine like terms: 1.892857143 + -1.892857143 = 0.000000000 0.000000000 + x = -2.140772796 + -1.892857143 x = -2.140772796 + -1.892857143 Combine like terms: -2.140772796 + -1.892857143 = -4.033629939 x = -4.033629939 Simplifying x = -4.033629939Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.247915653, -4.033629939}
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