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Simplifying 2.1x2 + -6x + 3 = 0 Reorder the terms: 3 + -6x + 2.1x2 = 0 Solving 3 + -6x + 2.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.1 the coefficient of the squared term: Divide each side by '2.1'. 1.428571429 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + -2.857142857x + -1.428571429 + x2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + -2.857142857x + x2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + -2.857142857x + x2 = 0 + -1.428571429 -2.857142857x + x2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 -2.857142857x + x2 = -1.428571429 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 = -1.428571429 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = -1.428571429 + 2.040816328 Combine like terms: -1.428571429 + 2.040816328 = 0.612244899 2.040816328 + -2.857142857x + x2 = 0.612244899 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 0.612244899 Calculate the square root of the right side: 0.782460797 Break this problem into two subproblems by setting (x + -1.428571429) equal to 0.782460797 and -0.782460797.Subproblem 1
x + -1.428571429 = 0.782460797 Simplifying x + -1.428571429 = 0.782460797 Reorder the terms: -1.428571429 + x = 0.782460797 Solving -1.428571429 + x = 0.782460797 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 = 0.782460797 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 0.782460797 + 1.428571429 x = 0.782460797 + 1.428571429 Combine like terms: 0.782460797 + 1.428571429 = 2.211032226 x = 2.211032226 Simplifying x = 2.211032226Subproblem 2
x + -1.428571429 = -0.782460797 Simplifying x + -1.428571429 = -0.782460797 Reorder the terms: -1.428571429 + x = -0.782460797 Solving -1.428571429 + x = -0.782460797 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 = -0.782460797 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -0.782460797 + 1.428571429 x = -0.782460797 + 1.428571429 Combine like terms: -0.782460797 + 1.428571429 = 0.646110632 x = 0.646110632 Simplifying x = 0.646110632Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.211032226, 0.646110632}
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