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Simplifying 3x2 + 11x + -3 = 0 Reorder the terms: -3 + 11x + 3x2 = 0 Solving -3 + 11x + 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 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 3.666666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 3.666666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3.666666667x + x2 = 0 + 1 3.666666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 3.666666667x + x2 = 1 The x term is 3.666666667x. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667x + 3.361111114 + x2 = 1 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = 1 + 3.361111114 Combine like terms: 1 + 3.361111114 = 4.361111114 3.361111114 + 3.666666667x + x2 = 4.361111114 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 4.361111114 Calculate the square root of the right side: 2.088327348 Break this problem into two subproblems by setting (x + 1.833333334) equal to 2.088327348 and -2.088327348.Subproblem 1
x + 1.833333334 = 2.088327348 Simplifying x + 1.833333334 = 2.088327348 Reorder the terms: 1.833333334 + x = 2.088327348 Solving 1.833333334 + x = 2.088327348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = 2.088327348 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 2.088327348 + -1.833333334 x = 2.088327348 + -1.833333334 Combine like terms: 2.088327348 + -1.833333334 = 0.254994014 x = 0.254994014 Simplifying x = 0.254994014Subproblem 2
x + 1.833333334 = -2.088327348 Simplifying x + 1.833333334 = -2.088327348 Reorder the terms: 1.833333334 + x = -2.088327348 Solving 1.833333334 + x = -2.088327348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = -2.088327348 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -2.088327348 + -1.833333334 x = -2.088327348 + -1.833333334 Combine like terms: -2.088327348 + -1.833333334 = -3.921660682 x = -3.921660682 Simplifying x = -3.921660682Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.254994014, -3.921660682}
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