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Simplifying 3x2 + -33x + 68 = 0 Reorder the terms: 68 + -33x + 3x2 = 0 Solving 68 + -33x + 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'. 22.66666667 + -11x + x2 = 0 Move the constant term to the right: Add '-22.66666667' to each side of the equation. 22.66666667 + -11x + -22.66666667 + x2 = 0 + -22.66666667 Reorder the terms: 22.66666667 + -22.66666667 + -11x + x2 = 0 + -22.66666667 Combine like terms: 22.66666667 + -22.66666667 = 0.00000000 0.00000000 + -11x + x2 = 0 + -22.66666667 -11x + x2 = 0 + -22.66666667 Combine like terms: 0 + -22.66666667 = -22.66666667 -11x + x2 = -22.66666667 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -22.66666667 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -22.66666667 + 30.25 Combine like terms: -22.66666667 + 30.25 = 7.58333333 30.25 + -11x + x2 = 7.58333333 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 7.58333333 Calculate the square root of the right side: 2.753785273 Break this problem into two subproblems by setting (x + -5.5) equal to 2.753785273 and -2.753785273.Subproblem 1
x + -5.5 = 2.753785273 Simplifying x + -5.5 = 2.753785273 Reorder the terms: -5.5 + x = 2.753785273 Solving -5.5 + x = 2.753785273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 2.753785273 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 2.753785273 + 5.5 x = 2.753785273 + 5.5 Combine like terms: 2.753785273 + 5.5 = 8.253785273 x = 8.253785273 Simplifying x = 8.253785273Subproblem 2
x + -5.5 = -2.753785273 Simplifying x + -5.5 = -2.753785273 Reorder the terms: -5.5 + x = -2.753785273 Solving -5.5 + x = -2.753785273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -2.753785273 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -2.753785273 + 5.5 x = -2.753785273 + 5.5 Combine like terms: -2.753785273 + 5.5 = 2.746214727 x = 2.746214727 Simplifying x = 2.746214727Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.253785273, 2.746214727}
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