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Simplifying 14x2 + -12x + 1 = 0 Reorder the terms: 1 + -12x + 14x2 = 0 Solving 1 + -12x + 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'. 0.07142857143 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + -0.8571428571x + -0.07142857143 + x2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + -0.8571428571x + x2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + -0.8571428571x + x2 = 0 + -0.07142857143 -0.8571428571x + x2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 -0.8571428571x + x2 = -0.07142857143 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = -0.07142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = -0.07142857143 + 0.1836734694 Combine like terms: -0.07142857143 + 0.1836734694 = 0.11224489797 0.1836734694 + -0.8571428571x + x2 = 0.11224489797 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 0.11224489797 Calculate the square root of the right side: 0.335029697 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 0.335029697 and -0.335029697.Subproblem 1
x + -0.4285714286 = 0.335029697 Simplifying x + -0.4285714286 = 0.335029697 Reorder the terms: -0.4285714286 + x = 0.335029697 Solving -0.4285714286 + x = 0.335029697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 0.335029697 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 0.335029697 + 0.4285714286 x = 0.335029697 + 0.4285714286 Combine like terms: 0.335029697 + 0.4285714286 = 0.7636011256 x = 0.7636011256 Simplifying x = 0.7636011256Subproblem 2
x + -0.4285714286 = -0.335029697 Simplifying x + -0.4285714286 = -0.335029697 Reorder the terms: -0.4285714286 + x = -0.335029697 Solving -0.4285714286 + x = -0.335029697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -0.335029697 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -0.335029697 + 0.4285714286 x = -0.335029697 + 0.4285714286 Combine like terms: -0.335029697 + 0.4285714286 = 0.0935417316 x = 0.0935417316 Simplifying x = 0.0935417316Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7636011256, 0.0935417316}
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