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Simplifying 3x2 + -1.1x + -3 = 0 Reorder the terms: -3 + -1.1x + 3x2 = 0 Solving -3 + -1.1x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -0.3666666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.3666666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.3666666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.3666666667x + x2 = 0 + 1 -0.3666666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.3666666667x + x2 = 1 The x term is -0.3666666667x. Take half its coefficient (-0.1833333334). Square it (0.03361111114) and add it to both sides. Add '0.03361111114' to each side of the equation. -0.3666666667x + 0.03361111114 + x2 = 1 + 0.03361111114 Reorder the terms: 0.03361111114 + -0.3666666667x + x2 = 1 + 0.03361111114 Combine like terms: 1 + 0.03361111114 = 1.03361111114 0.03361111114 + -0.3666666667x + x2 = 1.03361111114 Factor a perfect square on the left side: (x + -0.1833333334)(x + -0.1833333334) = 1.03361111114 Calculate the square root of the right side: 1.016666667 Break this problem into two subproblems by setting (x + -0.1833333334) equal to 1.016666667 and -1.016666667.Subproblem 1
x + -0.1833333334 = 1.016666667 Simplifying x + -0.1833333334 = 1.016666667 Reorder the terms: -0.1833333334 + x = 1.016666667 Solving -0.1833333334 + x = 1.016666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1833333334' to each side of the equation. -0.1833333334 + 0.1833333334 + x = 1.016666667 + 0.1833333334 Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000 0.0000000000 + x = 1.016666667 + 0.1833333334 x = 1.016666667 + 0.1833333334 Combine like terms: 1.016666667 + 0.1833333334 = 1.2000000004 x = 1.2000000004 Simplifying x = 1.2000000004Subproblem 2
x + -0.1833333334 = -1.016666667 Simplifying x + -0.1833333334 = -1.016666667 Reorder the terms: -0.1833333334 + x = -1.016666667 Solving -0.1833333334 + x = -1.016666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1833333334' to each side of the equation. -0.1833333334 + 0.1833333334 + x = -1.016666667 + 0.1833333334 Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000 0.0000000000 + x = -1.016666667 + 0.1833333334 x = -1.016666667 + 0.1833333334 Combine like terms: -1.016666667 + 0.1833333334 = -0.8333333336 x = -0.8333333336 Simplifying x = -0.8333333336Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2000000004, -0.8333333336}
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