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Simplifying 12x2 + -120x + 209 = 0 Reorder the terms: 209 + -120x + 12x2 = 0 Solving 209 + -120x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 17.41666667 + -10x + x2 = 0 Move the constant term to the right: Add '-17.41666667' to each side of the equation. 17.41666667 + -10x + -17.41666667 + x2 = 0 + -17.41666667 Reorder the terms: 17.41666667 + -17.41666667 + -10x + x2 = 0 + -17.41666667 Combine like terms: 17.41666667 + -17.41666667 = 0.00000000 0.00000000 + -10x + x2 = 0 + -17.41666667 -10x + x2 = 0 + -17.41666667 Combine like terms: 0 + -17.41666667 = -17.41666667 -10x + x2 = -17.41666667 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -17.41666667 + 25 Reorder the terms: 25 + -10x + x2 = -17.41666667 + 25 Combine like terms: -17.41666667 + 25 = 7.58333333 25 + -10x + x2 = 7.58333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 7.58333333 Calculate the square root of the right side: 2.753785273 Break this problem into two subproblems by setting (x + -5) equal to 2.753785273 and -2.753785273.Subproblem 1
x + -5 = 2.753785273 Simplifying x + -5 = 2.753785273 Reorder the terms: -5 + x = 2.753785273 Solving -5 + x = 2.753785273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.753785273 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.753785273 + 5 x = 2.753785273 + 5 Combine like terms: 2.753785273 + 5 = 7.753785273 x = 7.753785273 Simplifying x = 7.753785273Subproblem 2
x + -5 = -2.753785273 Simplifying x + -5 = -2.753785273 Reorder the terms: -5 + x = -2.753785273 Solving -5 + x = -2.753785273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.753785273 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.753785273 + 5 x = -2.753785273 + 5 Combine like terms: -2.753785273 + 5 = 2.246214727 x = 2.246214727 Simplifying x = 2.246214727Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.753785273, 2.246214727}
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