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Simplifying 24x2 + -39x + -5 = 0 Reorder the terms: -5 + -39x + 24x2 = 0 Solving -5 + -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'. -0.2083333333 + -1.625x + x2 = 0 Move the constant term to the right: Add '0.2083333333' to each side of the equation. -0.2083333333 + -1.625x + 0.2083333333 + x2 = 0 + 0.2083333333 Reorder the terms: -0.2083333333 + 0.2083333333 + -1.625x + x2 = 0 + 0.2083333333 Combine like terms: -0.2083333333 + 0.2083333333 = 0.0000000000 0.0000000000 + -1.625x + x2 = 0 + 0.2083333333 -1.625x + x2 = 0 + 0.2083333333 Combine like terms: 0 + 0.2083333333 = 0.2083333333 -1.625x + x2 = 0.2083333333 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 = 0.2083333333 + 0.66015625 Reorder the terms: 0.66015625 + -1.625x + x2 = 0.2083333333 + 0.66015625 Combine like terms: 0.2083333333 + 0.66015625 = 0.8684895833 0.66015625 + -1.625x + x2 = 0.8684895833 Factor a perfect square on the left side: (x + -0.8125)(x + -0.8125) = 0.8684895833 Calculate the square root of the right side: 0.931927885 Break this problem into two subproblems by setting (x + -0.8125) equal to 0.931927885 and -0.931927885.Subproblem 1
x + -0.8125 = 0.931927885 Simplifying x + -0.8125 = 0.931927885 Reorder the terms: -0.8125 + x = 0.931927885 Solving -0.8125 + x = 0.931927885 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 = 0.931927885 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = 0.931927885 + 0.8125 x = 0.931927885 + 0.8125 Combine like terms: 0.931927885 + 0.8125 = 1.744427885 x = 1.744427885 Simplifying x = 1.744427885Subproblem 2
x + -0.8125 = -0.931927885 Simplifying x + -0.8125 = -0.931927885 Reorder the terms: -0.8125 + x = -0.931927885 Solving -0.8125 + x = -0.931927885 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 = -0.931927885 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = -0.931927885 + 0.8125 x = -0.931927885 + 0.8125 Combine like terms: -0.931927885 + 0.8125 = -0.119427885 x = -0.119427885 Simplifying x = -0.119427885Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.744427885, -0.119427885}
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