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Simplifying 9x2 + -54x + -22 = 0 Reorder the terms: -22 + -54x + 9x2 = 0 Solving -22 + -54x + 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'. -2.444444444 + -6x + x2 = 0 Move the constant term to the right: Add '2.444444444' to each side of the equation. -2.444444444 + -6x + 2.444444444 + x2 = 0 + 2.444444444 Reorder the terms: -2.444444444 + 2.444444444 + -6x + x2 = 0 + 2.444444444 Combine like terms: -2.444444444 + 2.444444444 = 0.000000000 0.000000000 + -6x + x2 = 0 + 2.444444444 -6x + x2 = 0 + 2.444444444 Combine like terms: 0 + 2.444444444 = 2.444444444 -6x + x2 = 2.444444444 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 2.444444444 + 9 Reorder the terms: 9 + -6x + x2 = 2.444444444 + 9 Combine like terms: 2.444444444 + 9 = 11.444444444 9 + -6x + x2 = 11.444444444 Factor a perfect square on the left side: (x + -3)(x + -3) = 11.444444444 Calculate the square root of the right side: 3.382963855 Break this problem into two subproblems by setting (x + -3) equal to 3.382963855 and -3.382963855.Subproblem 1
x + -3 = 3.382963855 Simplifying x + -3 = 3.382963855 Reorder the terms: -3 + x = 3.382963855 Solving -3 + x = 3.382963855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.382963855 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.382963855 + 3 x = 3.382963855 + 3 Combine like terms: 3.382963855 + 3 = 6.382963855 x = 6.382963855 Simplifying x = 6.382963855Subproblem 2
x + -3 = -3.382963855 Simplifying x + -3 = -3.382963855 Reorder the terms: -3 + x = -3.382963855 Solving -3 + x = -3.382963855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.382963855 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.382963855 + 3 x = -3.382963855 + 3 Combine like terms: -3.382963855 + 3 = -0.382963855 x = -0.382963855 Simplifying x = -0.382963855Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.382963855, -0.382963855}
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