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Simplifying 11x2 + -1 = -12x Reorder the terms: -1 + 11x2 = -12x Solving -1 + 11x2 = -12x Solving for variable 'x'. Reorder the terms: -1 + 12x + 11x2 = -12x + 12x Combine like terms: -12x + 12x = 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 = 0.0777867815 x = 0.0777867815 Simplifying x = 0.0777867815Subproblem 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 = -1.1686958725 x = -1.1686958725 Simplifying x = -1.1686958725Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0777867815, -1.1686958725}
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