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Simplifying 3x2 + -11x + -40 = 0 Reorder the terms: -40 + -11x + 3x2 = 0 Solving -40 + -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'. -13.33333333 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -3.666666667x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -3.666666667x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -3.666666667x + x2 = 0 + 13.33333333 -3.666666667x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -3.666666667x + x2 = 13.33333333 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 = 13.33333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 13.33333333 + 3.361111114 Combine like terms: 13.33333333 + 3.361111114 = 16.694444444 3.361111114 + -3.666666667x + x2 = 16.694444444 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 16.694444444 Calculate the square root of the right side: 4.085883557 Break this problem into two subproblems by setting (x + -1.833333334) equal to 4.085883557 and -4.085883557.Subproblem 1
x + -1.833333334 = 4.085883557 Simplifying x + -1.833333334 = 4.085883557 Reorder the terms: -1.833333334 + x = 4.085883557 Solving -1.833333334 + x = 4.085883557 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 = 4.085883557 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 4.085883557 + 1.833333334 x = 4.085883557 + 1.833333334 Combine like terms: 4.085883557 + 1.833333334 = 5.919216891 x = 5.919216891 Simplifying x = 5.919216891Subproblem 2
x + -1.833333334 = -4.085883557 Simplifying x + -1.833333334 = -4.085883557 Reorder the terms: -1.833333334 + x = -4.085883557 Solving -1.833333334 + x = -4.085883557 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 = -4.085883557 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -4.085883557 + 1.833333334 x = -4.085883557 + 1.833333334 Combine like terms: -4.085883557 + 1.833333334 = -2.252550223 x = -2.252550223 Simplifying x = -2.252550223Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.919216891, -2.252550223}
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