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Simplifying 9(2 + -3x) + -29 = 8x(x + -23) (2 * 9 + -3x * 9) + -29 = 8x(x + -23) (18 + -27x) + -29 = 8x(x + -23) Reorder the terms: 18 + -29 + -27x = 8x(x + -23) Combine like terms: 18 + -29 = -11 -11 + -27x = 8x(x + -23) Reorder the terms: -11 + -27x = 8x(-23 + x) -11 + -27x = (-23 * 8x + x * 8x) -11 + -27x = (-184x + 8x2) Solving -11 + -27x = -184x + 8x2 Solving for variable 'x'. Combine like terms: -27x + 184x = 157x -11 + 157x + -8x2 = -184x + 8x2 + 184x + -8x2 Reorder the terms: -11 + 157x + -8x2 = -184x + 184x + 8x2 + -8x2 Combine like terms: -184x + 184x = 0 -11 + 157x + -8x2 = 0 + 8x2 + -8x2 -11 + 157x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -11 + 157x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.375 + -19.625x + x2 = 0 Move the constant term to the right: Add '-1.375' to each side of the equation. 1.375 + -19.625x + -1.375 + x2 = 0 + -1.375 Reorder the terms: 1.375 + -1.375 + -19.625x + x2 = 0 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + -19.625x + x2 = 0 + -1.375 -19.625x + x2 = 0 + -1.375 Combine like terms: 0 + -1.375 = -1.375 -19.625x + x2 = -1.375 The x term is -19.625x. Take half its coefficient (-9.8125). Square it (96.28515625) and add it to both sides. Add '96.28515625' to each side of the equation. -19.625x + 96.28515625 + x2 = -1.375 + 96.28515625 Reorder the terms: 96.28515625 + -19.625x + x2 = -1.375 + 96.28515625 Combine like terms: -1.375 + 96.28515625 = 94.91015625 96.28515625 + -19.625x + x2 = 94.91015625 Factor a perfect square on the left side: (x + -9.8125)(x + -9.8125) = 94.91015625 Calculate the square root of the right side: 9.742184367 Break this problem into two subproblems by setting (x + -9.8125) equal to 9.742184367 and -9.742184367.Subproblem 1
x + -9.8125 = 9.742184367 Simplifying x + -9.8125 = 9.742184367 Reorder the terms: -9.8125 + x = 9.742184367 Solving -9.8125 + x = 9.742184367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.8125' to each side of the equation. -9.8125 + 9.8125 + x = 9.742184367 + 9.8125 Combine like terms: -9.8125 + 9.8125 = 0.0000 0.0000 + x = 9.742184367 + 9.8125 x = 9.742184367 + 9.8125 Combine like terms: 9.742184367 + 9.8125 = 19.554684367 x = 19.554684367 Simplifying x = 19.554684367Subproblem 2
x + -9.8125 = -9.742184367 Simplifying x + -9.8125 = -9.742184367 Reorder the terms: -9.8125 + x = -9.742184367 Solving -9.8125 + x = -9.742184367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.8125' to each side of the equation. -9.8125 + 9.8125 + x = -9.742184367 + 9.8125 Combine like terms: -9.8125 + 9.8125 = 0.0000 0.0000 + x = -9.742184367 + 9.8125 x = -9.742184367 + 9.8125 Combine like terms: -9.742184367 + 9.8125 = 0.070315633 x = 0.070315633 Simplifying x = 0.070315633Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.554684367, 0.070315633}
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