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Simplifying -24x2 + -39x + 13 = 0 Reorder the terms: 13 + -39x + -24x2 = 0 Solving 13 + -39x + -24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. -0.5416666667 + 1.625x + x2 = 0 Move the constant term to the right: Add '0.5416666667' to each side of the equation. -0.5416666667 + 1.625x + 0.5416666667 + x2 = 0 + 0.5416666667 Reorder the terms: -0.5416666667 + 0.5416666667 + 1.625x + x2 = 0 + 0.5416666667 Combine like terms: -0.5416666667 + 0.5416666667 = 0.0000000000 0.0000000000 + 1.625x + x2 = 0 + 0.5416666667 1.625x + x2 = 0 + 0.5416666667 Combine like terms: 0 + 0.5416666667 = 0.5416666667 1.625x + x2 = 0.5416666667 The x term is 1.625x. Take half its coefficient (0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. 1.625x + 0.66015625 + x2 = 0.5416666667 + 0.66015625 Reorder the terms: 0.66015625 + 1.625x + x2 = 0.5416666667 + 0.66015625 Combine like terms: 0.5416666667 + 0.66015625 = 1.2018229167 0.66015625 + 1.625x + x2 = 1.2018229167 Factor a perfect square on the left side: (x + 0.8125)(x + 0.8125) = 1.2018229167 Calculate the square root of the right side: 1.096276843 Break this problem into two subproblems by setting (x + 0.8125) equal to 1.096276843 and -1.096276843.Subproblem 1
x + 0.8125 = 1.096276843 Simplifying x + 0.8125 = 1.096276843 Reorder the terms: 0.8125 + x = 1.096276843 Solving 0.8125 + x = 1.096276843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = 1.096276843 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = 1.096276843 + -0.8125 x = 1.096276843 + -0.8125 Combine like terms: 1.096276843 + -0.8125 = 0.283776843 x = 0.283776843 Simplifying x = 0.283776843Subproblem 2
x + 0.8125 = -1.096276843 Simplifying x + 0.8125 = -1.096276843 Reorder the terms: 0.8125 + x = -1.096276843 Solving 0.8125 + x = -1.096276843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = -1.096276843 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = -1.096276843 + -0.8125 x = -1.096276843 + -0.8125 Combine like terms: -1.096276843 + -0.8125 = -1.908776843 x = -1.908776843 Simplifying x = -1.908776843Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.283776843, -1.908776843}
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