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Simplifying 3x2 + -54x + 241 = 0 Reorder the terms: 241 + -54x + 3x2 = 0 Solving 241 + -54x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 80.33333333 + -18x + x2 = 0 Move the constant term to the right: Add '-80.33333333' to each side of the equation. 80.33333333 + -18x + -80.33333333 + x2 = 0 + -80.33333333 Reorder the terms: 80.33333333 + -80.33333333 + -18x + x2 = 0 + -80.33333333 Combine like terms: 80.33333333 + -80.33333333 = 0.00000000 0.00000000 + -18x + x2 = 0 + -80.33333333 -18x + x2 = 0 + -80.33333333 Combine like terms: 0 + -80.33333333 = -80.33333333 -18x + x2 = -80.33333333 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -80.33333333 + 81 Reorder the terms: 81 + -18x + x2 = -80.33333333 + 81 Combine like terms: -80.33333333 + 81 = 0.66666667 81 + -18x + x2 = 0.66666667 Factor a perfect square on the left side: (x + -9)(x + -9) = 0.66666667 Calculate the square root of the right side: 0.816496583 Break this problem into two subproblems by setting (x + -9) equal to 0.816496583 and -0.816496583.Subproblem 1
x + -9 = 0.816496583 Simplifying x + -9 = 0.816496583 Reorder the terms: -9 + x = 0.816496583 Solving -9 + x = 0.816496583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0.816496583 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0.816496583 + 9 x = 0.816496583 + 9 Combine like terms: 0.816496583 + 9 = 9.816496583 x = 9.816496583 Simplifying x = 9.816496583Subproblem 2
x + -9 = -0.816496583 Simplifying x + -9 = -0.816496583 Reorder the terms: -9 + x = -0.816496583 Solving -9 + x = -0.816496583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -0.816496583 + 9 Combine like terms: -9 + 9 = 0 0 + x = -0.816496583 + 9 x = -0.816496583 + 9 Combine like terms: -0.816496583 + 9 = 8.183503417 x = 8.183503417 Simplifying x = 8.183503417Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.816496583, 8.183503417}
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