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Simplifying 2x2 + -11x + 12 = 1 Reorder the terms: 12 + -11x + 2x2 = 1 Solving 12 + -11x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: 12 + -1 + -11x + 2x2 = 1 + -1 Combine like terms: 12 + -1 = 11 11 + -11x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 11 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -5.5x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -5.5x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -5.5x + x2 = 0 + -5.5 -5.5x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -5.5x + x2 = -5.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -5.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -5.5 + 7.5625 Combine like terms: -5.5 + 7.5625 = 2.0625 7.5625 + -5.5x + x2 = 2.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x + -2.75) equal to 1.436140662 and -1.436140662.Subproblem 1
x + -2.75 = 1.436140662 Simplifying x + -2.75 = 1.436140662 Reorder the terms: -2.75 + x = 1.436140662 Solving -2.75 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 1.436140662 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 1.436140662 + 2.75 x = 1.436140662 + 2.75 Combine like terms: 1.436140662 + 2.75 = 4.186140662 x = 4.186140662 Simplifying x = 4.186140662Subproblem 2
x + -2.75 = -1.436140662 Simplifying x + -2.75 = -1.436140662 Reorder the terms: -2.75 + x = -1.436140662 Solving -2.75 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -1.436140662 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -1.436140662 + 2.75 x = -1.436140662 + 2.75 Combine like terms: -1.436140662 + 2.75 = 1.313859338 x = 1.313859338 Simplifying x = 1.313859338Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.186140662, 1.313859338}
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