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Simplifying 9x2 + -55x + 11 = 0 Reorder the terms: 11 + -55x + 9x2 = 0 Solving 11 + -55x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.222222222 + -6.111111111x + x2 = 0 Move the constant term to the right: Add '-1.222222222' to each side of the equation. 1.222222222 + -6.111111111x + -1.222222222 + x2 = 0 + -1.222222222 Reorder the terms: 1.222222222 + -1.222222222 + -6.111111111x + x2 = 0 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + -6.111111111x + x2 = 0 + -1.222222222 -6.111111111x + x2 = 0 + -1.222222222 Combine like terms: 0 + -1.222222222 = -1.222222222 -6.111111111x + x2 = -1.222222222 The x term is -6.111111111x. Take half its coefficient (-3.055555556). Square it (9.336419756) and add it to both sides. Add '9.336419756' to each side of the equation. -6.111111111x + 9.336419756 + x2 = -1.222222222 + 9.336419756 Reorder the terms: 9.336419756 + -6.111111111x + x2 = -1.222222222 + 9.336419756 Combine like terms: -1.222222222 + 9.336419756 = 8.114197534 9.336419756 + -6.111111111x + x2 = 8.114197534 Factor a perfect square on the left side: (x + -3.055555556)(x + -3.055555556) = 8.114197534 Calculate the square root of the right side: 2.848543055 Break this problem into two subproblems by setting (x + -3.055555556) equal to 2.848543055 and -2.848543055.Subproblem 1
x + -3.055555556 = 2.848543055 Simplifying x + -3.055555556 = 2.848543055 Reorder the terms: -3.055555556 + x = 2.848543055 Solving -3.055555556 + x = 2.848543055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.055555556' to each side of the equation. -3.055555556 + 3.055555556 + x = 2.848543055 + 3.055555556 Combine like terms: -3.055555556 + 3.055555556 = 0.000000000 0.000000000 + x = 2.848543055 + 3.055555556 x = 2.848543055 + 3.055555556 Combine like terms: 2.848543055 + 3.055555556 = 5.904098611 x = 5.904098611 Simplifying x = 5.904098611Subproblem 2
x + -3.055555556 = -2.848543055 Simplifying x + -3.055555556 = -2.848543055 Reorder the terms: -3.055555556 + x = -2.848543055 Solving -3.055555556 + x = -2.848543055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.055555556' to each side of the equation. -3.055555556 + 3.055555556 + x = -2.848543055 + 3.055555556 Combine like terms: -3.055555556 + 3.055555556 = 0.000000000 0.000000000 + x = -2.848543055 + 3.055555556 x = -2.848543055 + 3.055555556 Combine like terms: -2.848543055 + 3.055555556 = 0.207012501 x = 0.207012501 Simplifying x = 0.207012501Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.904098611, 0.207012501}
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