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Simplifying 27x + -0.19x2 + -275 = 0 Reorder the terms: -275 + 27x + -0.19x2 = 0 Solving -275 + 27x + -0.19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.19 the coefficient of the squared term: Divide each side by '-0.19'. 1447.368421 + -142.1052632x + x2 = 0 Move the constant term to the right: Add '-1447.368421' to each side of the equation. 1447.368421 + -142.1052632x + -1447.368421 + x2 = 0 + -1447.368421 Reorder the terms: 1447.368421 + -1447.368421 + -142.1052632x + x2 = 0 + -1447.368421 Combine like terms: 1447.368421 + -1447.368421 = 0.000000 0.000000 + -142.1052632x + x2 = 0 + -1447.368421 -142.1052632x + x2 = 0 + -1447.368421 Combine like terms: 0 + -1447.368421 = -1447.368421 -142.1052632x + x2 = -1447.368421 The x term is -142.1052632x. Take half its coefficient (-71.0526316). Square it (5048.476457) and add it to both sides. Add '5048.476457' to each side of the equation. -142.1052632x + 5048.476457 + x2 = -1447.368421 + 5048.476457 Reorder the terms: 5048.476457 + -142.1052632x + x2 = -1447.368421 + 5048.476457 Combine like terms: -1447.368421 + 5048.476457 = 3601.108036 5048.476457 + -142.1052632x + x2 = 3601.108036 Factor a perfect square on the left side: (x + -71.0526316)(x + -71.0526316) = 3601.108036 Calculate the square root of the right side: 60.009232923 Break this problem into two subproblems by setting (x + -71.0526316) equal to 60.009232923 and -60.009232923.Subproblem 1
x + -71.0526316 = 60.009232923 Simplifying x + -71.0526316 = 60.009232923 Reorder the terms: -71.0526316 + x = 60.009232923 Solving -71.0526316 + x = 60.009232923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.0526316' to each side of the equation. -71.0526316 + 71.0526316 + x = 60.009232923 + 71.0526316 Combine like terms: -71.0526316 + 71.0526316 = 0.0000000 0.0000000 + x = 60.009232923 + 71.0526316 x = 60.009232923 + 71.0526316 Combine like terms: 60.009232923 + 71.0526316 = 131.061864523 x = 131.061864523 Simplifying x = 131.061864523Subproblem 2
x + -71.0526316 = -60.009232923 Simplifying x + -71.0526316 = -60.009232923 Reorder the terms: -71.0526316 + x = -60.009232923 Solving -71.0526316 + x = -60.009232923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.0526316' to each side of the equation. -71.0526316 + 71.0526316 + x = -60.009232923 + 71.0526316 Combine like terms: -71.0526316 + 71.0526316 = 0.0000000 0.0000000 + x = -60.009232923 + 71.0526316 x = -60.009232923 + 71.0526316 Combine like terms: -60.009232923 + 71.0526316 = 11.043398677 x = 11.043398677 Simplifying x = 11.043398677Solution
The solution to the problem is based on the solutions from the subproblems. x = {131.061864523, 11.043398677}
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