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Simplifying 24 = 3x2 + 13x Reorder the terms: 24 = 13x + 3x2 Solving 24 = 13x + 3x2 Solving for variable 'x'. Reorder the terms: 24 + -13x + -3x2 = 13x + -13x + 3x2 + -3x2 Combine like terms: 13x + -13x = 0 24 + -13x + -3x2 = 0 + 3x2 + -3x2 24 + -13x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 24 + -13x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -8 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 4.333333333x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 4.333333333x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4.333333333x + x2 = 0 + 8 4.333333333x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 4.333333333x + x2 = 8 The x term is 4.333333333x. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333x + 4.694444446 + x2 = 8 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = 8 + 4.694444446 Combine like terms: 8 + 4.694444446 = 12.694444446 4.694444446 + 4.333333333x + x2 = 12.694444446 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = 12.694444446 Calculate the square root of the right side: 3.562926388 Break this problem into two subproblems by setting (x + 2.166666667) equal to 3.562926388 and -3.562926388.Subproblem 1
x + 2.166666667 = 3.562926388 Simplifying x + 2.166666667 = 3.562926388 Reorder the terms: 2.166666667 + x = 3.562926388 Solving 2.166666667 + x = 3.562926388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 3.562926388 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 3.562926388 + -2.166666667 x = 3.562926388 + -2.166666667 Combine like terms: 3.562926388 + -2.166666667 = 1.396259721 x = 1.396259721 Simplifying x = 1.396259721Subproblem 2
x + 2.166666667 = -3.562926388 Simplifying x + 2.166666667 = -3.562926388 Reorder the terms: 2.166666667 + x = -3.562926388 Solving 2.166666667 + x = -3.562926388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -3.562926388 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -3.562926388 + -2.166666667 x = -3.562926388 + -2.166666667 Combine like terms: -3.562926388 + -2.166666667 = -5.729593055 x = -5.729593055 Simplifying x = -5.729593055Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.396259721, -5.729593055}
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