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Simplifying 14x2 = 1 + 2x Solving 14x2 = 1 + 2x Solving for variable 'x'. Reorder the terms: -1 + -2x + 14x2 = 1 + 2x + -1 + -2x Reorder the terms: -1 + -2x + 14x2 = 1 + -1 + 2x + -2x Combine like terms: 1 + -1 = 0 -1 + -2x + 14x2 = 0 + 2x + -2x -1 + -2x + 14x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -1 + -2x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.07142857143 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.07142857143' to each side of the equation. -0.07142857143 + -0.1428571429x + 0.07142857143 + x2 = 0 + 0.07142857143 Reorder the terms: -0.07142857143 + 0.07142857143 + -0.1428571429x + x2 = 0 + 0.07142857143 Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000 0.00000000000 + -0.1428571429x + x2 = 0 + 0.07142857143 -0.1428571429x + x2 = 0 + 0.07142857143 Combine like terms: 0 + 0.07142857143 = 0.07142857143 -0.1428571429x + x2 = 0.07142857143 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 0.07142857143 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 0.07142857143 + 0.005102040819 Combine like terms: 0.07142857143 + 0.005102040819 = 0.076530612249 0.005102040819 + -0.1428571429x + x2 = 0.076530612249 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 0.076530612249 Calculate the square root of the right side: 0.276641668 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 0.276641668 and -0.276641668.Subproblem 1
x + -0.07142857145 = 0.276641668 Simplifying x + -0.07142857145 = 0.276641668 Reorder the terms: -0.07142857145 + x = 0.276641668 Solving -0.07142857145 + x = 0.276641668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 0.276641668 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.276641668 + 0.07142857145 x = 0.276641668 + 0.07142857145 Combine like terms: 0.276641668 + 0.07142857145 = 0.34807023945 x = 0.34807023945 Simplifying x = 0.34807023945Subproblem 2
x + -0.07142857145 = -0.276641668 Simplifying x + -0.07142857145 = -0.276641668 Reorder the terms: -0.07142857145 + x = -0.276641668 Solving -0.07142857145 + x = -0.276641668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -0.276641668 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.276641668 + 0.07142857145 x = -0.276641668 + 0.07142857145 Combine like terms: -0.276641668 + 0.07142857145 = -0.20521309655 x = -0.20521309655 Simplifying x = -0.20521309655Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34807023945, -0.20521309655}
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