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Simplifying 0.0714285714x2 + -0.1428571429x = 1 Reorder the terms: -0.1428571429x + 0.0714285714x2 = 1 Solving -0.1428571429x + 0.0714285714x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -0.1428571429x + 0.0714285714x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -0.1428571429x + 0.0714285714x2 = 0 Begin completing the square. Divide all terms by 0.0714285714 the coefficient of the squared term: Divide each side by '0.0714285714'. -14.00000001 + -2.000000001x + x2 = 0 Move the constant term to the right: Add '14.00000001' to each side of the equation. -14.00000001 + -2.000000001x + 14.00000001 + x2 = 0 + 14.00000001 Reorder the terms: -14.00000001 + 14.00000001 + -2.000000001x + x2 = 0 + 14.00000001 Combine like terms: -14.00000001 + 14.00000001 = 0.00000000 0.00000000 + -2.000000001x + x2 = 0 + 14.00000001 -2.000000001x + x2 = 0 + 14.00000001 Combine like terms: 0 + 14.00000001 = 14.00000001 -2.000000001x + x2 = 14.00000001 The x term is -2.000000001x. Take half its coefficient (-1.000000001). Square it (1.000000002) and add it to both sides. Add '1.000000002' to each side of the equation. -2.000000001x + 1.000000002 + x2 = 14.00000001 + 1.000000002 Reorder the terms: 1.000000002 + -2.000000001x + x2 = 14.00000001 + 1.000000002 Combine like terms: 14.00000001 + 1.000000002 = 15.000000012 1.000000002 + -2.000000001x + x2 = 15.000000012 Factor a perfect square on the left side: (x + -1.000000001)(x + -1.000000001) = 15.000000012 Calculate the square root of the right side: 3.872983348 Break this problem into two subproblems by setting (x + -1.000000001) equal to 3.872983348 and -3.872983348.Subproblem 1
x + -1.000000001 = 3.872983348 Simplifying x + -1.000000001 = 3.872983348 Reorder the terms: -1.000000001 + x = 3.872983348 Solving -1.000000001 + x = 3.872983348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.000000001' to each side of the equation. -1.000000001 + 1.000000001 + x = 3.872983348 + 1.000000001 Combine like terms: -1.000000001 + 1.000000001 = 0.000000000 0.000000000 + x = 3.872983348 + 1.000000001 x = 3.872983348 + 1.000000001 Combine like terms: 3.872983348 + 1.000000001 = 4.872983349 x = 4.872983349 Simplifying x = 4.872983349Subproblem 2
x + -1.000000001 = -3.872983348 Simplifying x + -1.000000001 = -3.872983348 Reorder the terms: -1.000000001 + x = -3.872983348 Solving -1.000000001 + x = -3.872983348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.000000001' to each side of the equation. -1.000000001 + 1.000000001 + x = -3.872983348 + 1.000000001 Combine like terms: -1.000000001 + 1.000000001 = 0.000000000 0.000000000 + x = -3.872983348 + 1.000000001 x = -3.872983348 + 1.000000001 Combine like terms: -3.872983348 + 1.000000001 = -2.872983347 x = -2.872983347 Simplifying x = -2.872983347Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.872983349, -2.872983347}
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