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Simplifying (2x + -5) = x2 + -27x + 31 Reorder the terms: (-5 + 2x) = x2 + -27x + 31 Remove parenthesis around (-5 + 2x) -5 + 2x = x2 + -27x + 31 Reorder the terms: -5 + 2x = 31 + -27x + x2 Solving -5 + 2x = 31 + -27x + x2 Solving for variable 'x'. Reorder the terms: -5 + -31 + 2x + 27x + -1x2 = 31 + -27x + x2 + -31 + 27x + -1x2 Combine like terms: -5 + -31 = -36 -36 + 2x + 27x + -1x2 = 31 + -27x + x2 + -31 + 27x + -1x2 Combine like terms: 2x + 27x = 29x -36 + 29x + -1x2 = 31 + -27x + x2 + -31 + 27x + -1x2 Reorder the terms: -36 + 29x + -1x2 = 31 + -31 + -27x + 27x + x2 + -1x2 Combine like terms: 31 + -31 = 0 -36 + 29x + -1x2 = 0 + -27x + 27x + x2 + -1x2 -36 + 29x + -1x2 = -27x + 27x + x2 + -1x2 Combine like terms: -27x + 27x = 0 -36 + 29x + -1x2 = 0 + x2 + -1x2 -36 + 29x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -36 + 29x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 36 + -29x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -29x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -29x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -29x + x2 = 0 + -36 -29x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -29x + x2 = -36 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -36 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -36 + 210.25 Combine like terms: -36 + 210.25 = 174.25 210.25 + -29x + x2 = 174.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (x + -14.5) equal to 13.200378782 and -13.200378782.Subproblem 1
x + -14.5 = 13.200378782 Simplifying x + -14.5 = 13.200378782 Reorder the terms: -14.5 + x = 13.200378782 Solving -14.5 + x = 13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 13.200378782 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 13.200378782 + 14.5 x = 13.200378782 + 14.5 Combine like terms: 13.200378782 + 14.5 = 27.700378782 x = 27.700378782 Simplifying x = 27.700378782Subproblem 2
x + -14.5 = -13.200378782 Simplifying x + -14.5 = -13.200378782 Reorder the terms: -14.5 + x = -13.200378782 Solving -14.5 + x = -13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -13.200378782 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -13.200378782 + 14.5 x = -13.200378782 + 14.5 Combine like terms: -13.200378782 + 14.5 = 1.299621218 x = 1.299621218 Simplifying x = 1.299621218Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.700378782, 1.299621218}
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