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Simplifying x2 + 27x = 22.8035085 Reorder the terms: 27x + x2 = 22.8035085 Solving 27x + x2 = 22.8035085 Solving for variable 'x'. Reorder the terms: -22.8035085 + 27x + x2 = 22.8035085 + -22.8035085 Combine like terms: 22.8035085 + -22.8035085 = 0.0000000 -22.8035085 + 27x + x2 = 0.0000000 Begin completing the square. Move the constant term to the right: Add '22.8035085' to each side of the equation. -22.8035085 + 27x + 22.8035085 + x2 = 0.0000000 + 22.8035085 Reorder the terms: -22.8035085 + 22.8035085 + 27x + x2 = 0.0000000 + 22.8035085 Combine like terms: -22.8035085 + 22.8035085 = 0.0000000 0.0000000 + 27x + x2 = 0.0000000 + 22.8035085 27x + x2 = 0.0000000 + 22.8035085 Combine like terms: 0.0000000 + 22.8035085 = 22.8035085 27x + x2 = 22.8035085 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = 22.8035085 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 22.8035085 + 182.25 Combine like terms: 22.8035085 + 182.25 = 205.0535085 182.25 + 27x + x2 = 205.0535085 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 205.0535085 Calculate the square root of the right side: 14.319689539 Break this problem into two subproblems by setting (x + 13.5) equal to 14.319689539 and -14.319689539.Subproblem 1
x + 13.5 = 14.319689539 Simplifying x + 13.5 = 14.319689539 Reorder the terms: 13.5 + x = 14.319689539 Solving 13.5 + x = 14.319689539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 14.319689539 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 14.319689539 + -13.5 x = 14.319689539 + -13.5 Combine like terms: 14.319689539 + -13.5 = 0.819689539 x = 0.819689539 Simplifying x = 0.819689539Subproblem 2
x + 13.5 = -14.319689539 Simplifying x + 13.5 = -14.319689539 Reorder the terms: 13.5 + x = -14.319689539 Solving 13.5 + x = -14.319689539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -14.319689539 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -14.319689539 + -13.5 x = -14.319689539 + -13.5 Combine like terms: -14.319689539 + -13.5 = -27.819689539 x = -27.819689539 Simplifying x = -27.819689539Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.819689539, -27.819689539}
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