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Simplifying 4x2 + 39x + -24 = 0 Reorder the terms: -24 + 39x + 4x2 = 0 Solving -24 + 39x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6 + 9.75x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 9.75x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 9.75x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 9.75x + x2 = 0 + 6 9.75x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 9.75x + x2 = 6 The x term is 9.75x. Take half its coefficient (4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. 9.75x + 23.765625 + x2 = 6 + 23.765625 Reorder the terms: 23.765625 + 9.75x + x2 = 6 + 23.765625 Combine like terms: 6 + 23.765625 = 29.765625 23.765625 + 9.75x + x2 = 29.765625 Factor a perfect square on the left side: (x + 4.875)(x + 4.875) = 29.765625 Calculate the square root of the right side: 5.455788211 Break this problem into two subproblems by setting (x + 4.875) equal to 5.455788211 and -5.455788211.Subproblem 1
x + 4.875 = 5.455788211 Simplifying x + 4.875 = 5.455788211 Reorder the terms: 4.875 + x = 5.455788211 Solving 4.875 + x = 5.455788211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.875' to each side of the equation. 4.875 + -4.875 + x = 5.455788211 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + x = 5.455788211 + -4.875 x = 5.455788211 + -4.875 Combine like terms: 5.455788211 + -4.875 = 0.580788211 x = 0.580788211 Simplifying x = 0.580788211Subproblem 2
x + 4.875 = -5.455788211 Simplifying x + 4.875 = -5.455788211 Reorder the terms: 4.875 + x = -5.455788211 Solving 4.875 + x = -5.455788211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.875' to each side of the equation. 4.875 + -4.875 + x = -5.455788211 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + x = -5.455788211 + -4.875 x = -5.455788211 + -4.875 Combine like terms: -5.455788211 + -4.875 = -10.330788211 x = -10.330788211 Simplifying x = -10.330788211Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.580788211, -10.330788211}
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