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Simplifying 14x2 + 8x + 1 = 0 Reorder the terms: 1 + 8x + 14x2 = 0 Solving 1 + 8x + 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 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + 0.5714285714x + -0.07142857143 + x2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + 0.5714285714x + x2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + 0.5714285714x + x2 = 0 + -0.07142857143 0.5714285714x + x2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 0.5714285714x + x2 = -0.07142857143 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = -0.07142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = -0.07142857143 + 0.08163265305 Combine like terms: -0.07142857143 + 0.08163265305 = 0.01020408162 0.08163265305 + 0.5714285714x + x2 = 0.01020408162 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.01020408162 Calculate the square root of the right side: 0.101015254 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.101015254 and -0.101015254.Subproblem 1
x + 0.2857142857 = 0.101015254 Simplifying x + 0.2857142857 = 0.101015254 Reorder the terms: 0.2857142857 + x = 0.101015254 Solving 0.2857142857 + x = 0.101015254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 0.101015254 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.101015254 + -0.2857142857 x = 0.101015254 + -0.2857142857 Combine like terms: 0.101015254 + -0.2857142857 = -0.1846990317 x = -0.1846990317 Simplifying x = -0.1846990317Subproblem 2
x + 0.2857142857 = -0.101015254 Simplifying x + 0.2857142857 = -0.101015254 Reorder the terms: 0.2857142857 + x = -0.101015254 Solving 0.2857142857 + x = -0.101015254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -0.101015254 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.101015254 + -0.2857142857 x = -0.101015254 + -0.2857142857 Combine like terms: -0.101015254 + -0.2857142857 = -0.3867295397 x = -0.3867295397 Simplifying x = -0.3867295397Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1846990317, -0.3867295397}
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