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Simplifying 3x2 + 7x + -24 = -13x Reorder the terms: -24 + 7x + 3x2 = -13x Solving -24 + 7x + 3x2 = -13x Solving for variable 'x'. Reorder the terms: -24 + 7x + 13x + 3x2 = -13x + 13x Combine like terms: 7x + 13x = 20x -24 + 20x + 3x2 = -13x + 13x Combine like terms: -13x + 13x = 0 -24 + 20x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 6.666666667x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 6.666666667x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6.666666667x + x2 = 0 + 8 6.666666667x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 6.666666667x + x2 = 8 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = 8 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 8 + 11.11111112 Combine like terms: 8 + 11.11111112 = 19.11111112 11.11111112 + 6.666666667x + x2 = 19.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 19.11111112 Calculate the square root of the right side: 4.371625684 Break this problem into two subproblems by setting (x + 3.333333334) equal to 4.371625684 and -4.371625684.Subproblem 1
x + 3.333333334 = 4.371625684 Simplifying x + 3.333333334 = 4.371625684 Reorder the terms: 3.333333334 + x = 4.371625684 Solving 3.333333334 + x = 4.371625684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 4.371625684 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 4.371625684 + -3.333333334 x = 4.371625684 + -3.333333334 Combine like terms: 4.371625684 + -3.333333334 = 1.03829235 x = 1.03829235 Simplifying x = 1.03829235Subproblem 2
x + 3.333333334 = -4.371625684 Simplifying x + 3.333333334 = -4.371625684 Reorder the terms: 3.333333334 + x = -4.371625684 Solving 3.333333334 + x = -4.371625684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -4.371625684 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -4.371625684 + -3.333333334 x = -4.371625684 + -3.333333334 Combine like terms: -4.371625684 + -3.333333334 = -7.704959018 x = -7.704959018 Simplifying x = -7.704959018Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.03829235, -7.704959018}
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