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Simplifying x2 + -11x + 2 = 121x2 Reorder the terms: 2 + -11x + x2 = 121x2 Solving 2 + -11x + x2 = 121x2 Solving for variable 'x'. Combine like terms: x2 + -121x2 = -120x2 2 + -11x + -120x2 = 121x2 + -121x2 Combine like terms: 121x2 + -121x2 = 0 2 + -11x + -120x2 = 0 Begin completing the square. Divide all terms by -120 the coefficient of the squared term: Divide each side by '-120'. -0.01666666667 + 0.09166666667x + x2 = 0.0 Move the constant term to the right: Add '0.01666666667' to each side of the equation. -0.01666666667 + 0.09166666667x + 0.01666666667 + x2 = 0.0 + 0.01666666667 Reorder the terms: -0.01666666667 + 0.01666666667 + 0.09166666667x + x2 = 0.0 + 0.01666666667 Combine like terms: -0.01666666667 + 0.01666666667 = 0.00000000000 0.00000000000 + 0.09166666667x + x2 = 0.0 + 0.01666666667 0.09166666667x + x2 = 0.0 + 0.01666666667 Combine like terms: 0.0 + 0.01666666667 = 0.01666666667 0.09166666667x + x2 = 0.01666666667 The x term is 0.09166666667x. Take half its coefficient (0.04583333334). Square it (0.002100694445) and add it to both sides. Add '0.002100694445' to each side of the equation. 0.09166666667x + 0.002100694445 + x2 = 0.01666666667 + 0.002100694445 Reorder the terms: 0.002100694445 + 0.09166666667x + x2 = 0.01666666667 + 0.002100694445 Combine like terms: 0.01666666667 + 0.002100694445 = 0.018767361115 0.002100694445 + 0.09166666667x + x2 = 0.018767361115 Factor a perfect square on the left side: (x + 0.04583333334)(x + 0.04583333334) = 0.018767361115 Calculate the square root of the right side: 0.136994019 Break this problem into two subproblems by setting (x + 0.04583333334) equal to 0.136994019 and -0.136994019.Subproblem 1
x + 0.04583333334 = 0.136994019 Simplifying x + 0.04583333334 = 0.136994019 Reorder the terms: 0.04583333334 + x = 0.136994019 Solving 0.04583333334 + x = 0.136994019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04583333334' to each side of the equation. 0.04583333334 + -0.04583333334 + x = 0.136994019 + -0.04583333334 Combine like terms: 0.04583333334 + -0.04583333334 = 0.00000000000 0.00000000000 + x = 0.136994019 + -0.04583333334 x = 0.136994019 + -0.04583333334 Combine like terms: 0.136994019 + -0.04583333334 = 0.09116068566 x = 0.09116068566 Simplifying x = 0.09116068566Subproblem 2
x + 0.04583333334 = -0.136994019 Simplifying x + 0.04583333334 = -0.136994019 Reorder the terms: 0.04583333334 + x = -0.136994019 Solving 0.04583333334 + x = -0.136994019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04583333334' to each side of the equation. 0.04583333334 + -0.04583333334 + x = -0.136994019 + -0.04583333334 Combine like terms: 0.04583333334 + -0.04583333334 = 0.00000000000 0.00000000000 + x = -0.136994019 + -0.04583333334 x = -0.136994019 + -0.04583333334 Combine like terms: -0.136994019 + -0.04583333334 = -0.18282735234 x = -0.18282735234 Simplifying x = -0.18282735234Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.09116068566, -0.18282735234}
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