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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 = 0.333333336 1.777777780 + 2.666666667x + x2 = 0.333333336 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 0.333333336 Calculate the square root of the right side: 0.577350271 Break this problem into two subproblems by setting (x + 1.333333334) equal to 0.577350271 and -0.577350271.Subproblem 1
x + 1.333333334 = 0.577350271 Simplifying x + 1.333333334 = 0.577350271 Reorder the terms: 1.333333334 + x = 0.577350271 Solving 1.333333334 + x = 0.577350271 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 = 0.577350271 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 0.577350271 + -1.333333334 x = 0.577350271 + -1.333333334 Combine like terms: 0.577350271 + -1.333333334 = -0.755983063 x = -0.755983063 Simplifying x = -0.755983063Subproblem 2
x + 1.333333334 = -0.577350271 Simplifying x + 1.333333334 = -0.577350271 Reorder the terms: 1.333333334 + x = -0.577350271 Solving 1.333333334 + x = -0.577350271 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 = -0.577350271 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -0.577350271 + -1.333333334 x = -0.577350271 + -1.333333334 Combine like terms: -0.577350271 + -1.333333334 = -1.910683605 x = -1.910683605 Simplifying x = -1.910683605Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.755983063, -1.910683605}
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