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Simplifying 27x + x2 = 506.16 Solving 27x + x2 = 506.16 Solving for variable 'x'. Reorder the terms: -506.16 + 27x + x2 = 506.16 + -506.16 Combine like terms: 506.16 + -506.16 = 0.00 -506.16 + 27x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '506.16' to each side of the equation. -506.16 + 27x + 506.16 + x2 = 0.00 + 506.16 Reorder the terms: -506.16 + 506.16 + 27x + x2 = 0.00 + 506.16 Combine like terms: -506.16 + 506.16 = 0.00 0.00 + 27x + x2 = 0.00 + 506.16 27x + x2 = 0.00 + 506.16 Combine like terms: 0.00 + 506.16 = 506.16 27x + x2 = 506.16 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 = 506.16 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 506.16 + 182.25 Combine like terms: 506.16 + 182.25 = 688.41 182.25 + 27x + x2 = 688.41 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 688.41 Calculate the square root of the right side: 26.237568485 Break this problem into two subproblems by setting (x + 13.5) equal to 26.237568485 and -26.237568485.Subproblem 1
x + 13.5 = 26.237568485 Simplifying x + 13.5 = 26.237568485 Reorder the terms: 13.5 + x = 26.237568485 Solving 13.5 + x = 26.237568485 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 = 26.237568485 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 26.237568485 + -13.5 x = 26.237568485 + -13.5 Combine like terms: 26.237568485 + -13.5 = 12.737568485 x = 12.737568485 Simplifying x = 12.737568485Subproblem 2
x + 13.5 = -26.237568485 Simplifying x + 13.5 = -26.237568485 Reorder the terms: 13.5 + x = -26.237568485 Solving 13.5 + x = -26.237568485 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 = -26.237568485 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -26.237568485 + -13.5 x = -26.237568485 + -13.5 Combine like terms: -26.237568485 + -13.5 = -39.737568485 x = -39.737568485 Simplifying x = -39.737568485Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.737568485, -39.737568485}
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