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Simplifying 11x2 + -12x = 1 Reorder the terms: -12x + 11x2 = 1 Solving -12x + 11x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -12x + 11x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -12x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.09090909091 + -1.090909091x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -1.090909091x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -1.090909091x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -1.090909091x + x2 = 0 + 0.09090909091 -1.090909091x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -1.090909091x + x2 = 0.09090909091 The x term is -1.090909091x. Take half its coefficient (-0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. -1.090909091x + 0.2975206612 + x2 = 0.09090909091 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091x + x2 = 0.09090909091 + 0.2975206612 Combine like terms: 0.09090909091 + 0.2975206612 = 0.38842975211 0.2975206612 + -1.090909091x + x2 = 0.38842975211 Factor a perfect square on the left side: (x + -0.5454545455)(x + -0.5454545455) = 0.38842975211 Calculate the square root of the right side: 0.623241327 Break this problem into two subproblems by setting (x + -0.5454545455) equal to 0.623241327 and -0.623241327.Subproblem 1
x + -0.5454545455 = 0.623241327 Simplifying x + -0.5454545455 = 0.623241327 Reorder the terms: -0.5454545455 + x = 0.623241327 Solving -0.5454545455 + x = 0.623241327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + x = 0.623241327 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = 0.623241327 + 0.5454545455 x = 0.623241327 + 0.5454545455 Combine like terms: 0.623241327 + 0.5454545455 = 1.1686958725 x = 1.1686958725 Simplifying x = 1.1686958725Subproblem 2
x + -0.5454545455 = -0.623241327 Simplifying x + -0.5454545455 = -0.623241327 Reorder the terms: -0.5454545455 + x = -0.623241327 Solving -0.5454545455 + x = -0.623241327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + x = -0.623241327 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = -0.623241327 + 0.5454545455 x = -0.623241327 + 0.5454545455 Combine like terms: -0.623241327 + 0.5454545455 = -0.0777867815 x = -0.0777867815 Simplifying x = -0.0777867815Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1686958725, -0.0777867815}
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