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Simplifying 3x2 + -11x + -120 = 0 Reorder the terms: -120 + -11x + 3x2 = 0 Solving -120 + -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'. -40 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -3.666666667x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -3.666666667x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -3.666666667x + x2 = 0 + 40 -3.666666667x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -3.666666667x + x2 = 40 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 = 40 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 40 + 3.361111114 Combine like terms: 40 + 3.361111114 = 43.361111114 3.361111114 + -3.666666667x + x2 = 43.361111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 43.361111114 Calculate the square root of the right side: 6.584915422 Break this problem into two subproblems by setting (x + -1.833333334) equal to 6.584915422 and -6.584915422.Subproblem 1
x + -1.833333334 = 6.584915422 Simplifying x + -1.833333334 = 6.584915422 Reorder the terms: -1.833333334 + x = 6.584915422 Solving -1.833333334 + x = 6.584915422 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 = 6.584915422 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 6.584915422 + 1.833333334 x = 6.584915422 + 1.833333334 Combine like terms: 6.584915422 + 1.833333334 = 8.418248756 x = 8.418248756 Simplifying x = 8.418248756Subproblem 2
x + -1.833333334 = -6.584915422 Simplifying x + -1.833333334 = -6.584915422 Reorder the terms: -1.833333334 + x = -6.584915422 Solving -1.833333334 + x = -6.584915422 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 = -6.584915422 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -6.584915422 + 1.833333334 x = -6.584915422 + 1.833333334 Combine like terms: -6.584915422 + 1.833333334 = -4.751582088 x = -4.751582088 Simplifying x = -4.751582088Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.418248756, -4.751582088}
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