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Simplifying 8x2 + -34x + 24 = 11 Reorder the terms: 24 + -34x + 8x2 = 11 Solving 24 + -34x + 8x2 = 11 Solving for variable 'x'. Reorder the terms: 24 + -11 + -34x + 8x2 = 11 + -11 Combine like terms: 24 + -11 = 13 13 + -34x + 8x2 = 11 + -11 Combine like terms: 11 + -11 = 0 13 + -34x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.625 + -4.25x + x2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -4.25x + -1.625 + x2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + -4.25x + x2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -4.25x + x2 = 0 + -1.625 -4.25x + x2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 -4.25x + x2 = -1.625 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = -1.625 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -1.625 + 4.515625 Combine like terms: -1.625 + 4.515625 = 2.890625 4.515625 + -4.25x + x2 = 2.890625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (x + -2.125) equal to 1.700183814 and -1.700183814.Subproblem 1
x + -2.125 = 1.700183814 Simplifying x + -2.125 = 1.700183814 Reorder the terms: -2.125 + x = 1.700183814 Solving -2.125 + x = 1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 1.700183814 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 1.700183814 + 2.125 x = 1.700183814 + 2.125 Combine like terms: 1.700183814 + 2.125 = 3.825183814 x = 3.825183814 Simplifying x = 3.825183814Subproblem 2
x + -2.125 = -1.700183814 Simplifying x + -2.125 = -1.700183814 Reorder the terms: -2.125 + x = -1.700183814 Solving -2.125 + x = -1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -1.700183814 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -1.700183814 + 2.125 x = -1.700183814 + 2.125 Combine like terms: -1.700183814 + 2.125 = 0.424816186 x = 0.424816186 Simplifying x = 0.424816186Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.825183814, 0.424816186}
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