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Simplifying 0.35x2 + -1x + 0.35 = 0 Reorder the terms: 0.35 + -1x + 0.35x2 = 0 Solving 0.35 + -1x + 0.35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.35 the coefficient of the squared term: Divide each side by '0.35'. 1 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.857142857x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.857142857x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.857142857x + x2 = 0 + -1 -2.857142857x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.857142857x + x2 = -1 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = -1 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = -1 + 2.040816328 Combine like terms: -1 + 2.040816328 = 1.040816328 2.040816328 + -2.857142857x + x2 = 1.040816328 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 1.040816328 Calculate the square root of the right side: 1.020204062 Break this problem into two subproblems by setting (x + -1.428571429) equal to 1.020204062 and -1.020204062.Subproblem 1
x + -1.428571429 = 1.020204062 Simplifying x + -1.428571429 = 1.020204062 Reorder the terms: -1.428571429 + x = 1.020204062 Solving -1.428571429 + x = 1.020204062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 1.020204062 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 1.020204062 + 1.428571429 x = 1.020204062 + 1.428571429 Combine like terms: 1.020204062 + 1.428571429 = 2.448775491 x = 2.448775491 Simplifying x = 2.448775491Subproblem 2
x + -1.428571429 = -1.020204062 Simplifying x + -1.428571429 = -1.020204062 Reorder the terms: -1.428571429 + x = -1.020204062 Solving -1.428571429 + x = -1.020204062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -1.020204062 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -1.020204062 + 1.428571429 x = -1.020204062 + 1.428571429 Combine like terms: -1.020204062 + 1.428571429 = 0.408367367 x = 0.408367367 Simplifying x = 0.408367367Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.448775491, 0.408367367}
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