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Simplifying 9x2 + 24x + -13 = 0 Reorder the terms: -13 + 24x + 9x2 = 0 Solving -13 + 24x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.444444444 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '1.444444444' to each side of the equation. -1.444444444 + 2.666666667x + 1.444444444 + x2 = 0 + 1.444444444 Reorder the terms: -1.444444444 + 1.444444444 + 2.666666667x + x2 = 0 + 1.444444444 Combine like terms: -1.444444444 + 1.444444444 = 0.000000000 0.000000000 + 2.666666667x + x2 = 0 + 1.444444444 2.666666667x + x2 = 0 + 1.444444444 Combine like terms: 0 + 1.444444444 = 1.444444444 2.666666667x + x2 = 1.444444444 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 1.444444444 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 1.444444444 + 1.777777780 Combine like terms: 1.444444444 + 1.777777780 = 3.222222224 1.777777780 + 2.666666667x + x2 = 3.222222224 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 3.222222224 Calculate the square root of the right side: 1.795054936 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.795054936 and -1.795054936.Subproblem 1
x + 1.333333334 = 1.795054936 Simplifying x + 1.333333334 = 1.795054936 Reorder the terms: 1.333333334 + x = 1.795054936 Solving 1.333333334 + x = 1.795054936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 1.795054936 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.795054936 + -1.333333334 x = 1.795054936 + -1.333333334 Combine like terms: 1.795054936 + -1.333333334 = 0.461721602 x = 0.461721602 Simplifying x = 0.461721602Subproblem 2
x + 1.333333334 = -1.795054936 Simplifying x + 1.333333334 = -1.795054936 Reorder the terms: 1.333333334 + x = -1.795054936 Solving 1.333333334 + x = -1.795054936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -1.795054936 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.795054936 + -1.333333334 x = -1.795054936 + -1.333333334 Combine like terms: -1.795054936 + -1.333333334 = -3.12838827 x = -3.12838827 Simplifying x = -3.12838827Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.461721602, -3.12838827}
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