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Simplifying 4x2 + -11x + -24 = 0 Reorder the terms: -24 + -11x + 4x2 = 0 Solving -24 + -11x + 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 + -2.75x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2.75x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -2.75x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2.75x + x2 = 0 + 6 -2.75x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2.75x + x2 = 6 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 6 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 6 + 1.890625 Combine like terms: 6 + 1.890625 = 7.890625 1.890625 + -2.75x + x2 = 7.890625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 7.890625 Calculate the square root of the right side: 2.809025632 Break this problem into two subproblems by setting (x + -1.375) equal to 2.809025632 and -2.809025632.Subproblem 1
x + -1.375 = 2.809025632 Simplifying x + -1.375 = 2.809025632 Reorder the terms: -1.375 + x = 2.809025632 Solving -1.375 + x = 2.809025632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.809025632 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.809025632 + 1.375 x = 2.809025632 + 1.375 Combine like terms: 2.809025632 + 1.375 = 4.184025632 x = 4.184025632 Simplifying x = 4.184025632Subproblem 2
x + -1.375 = -2.809025632 Simplifying x + -1.375 = -2.809025632 Reorder the terms: -1.375 + x = -2.809025632 Solving -1.375 + x = -2.809025632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.809025632 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.809025632 + 1.375 x = -2.809025632 + 1.375 Combine like terms: -2.809025632 + 1.375 = -1.434025632 x = -1.434025632 Simplifying x = -1.434025632Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.184025632, -1.434025632}
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