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Simplifying x2 + 56 = 12x(x + 1) Reorder the terms: 56 + x2 = 12x(x + 1) Reorder the terms: 56 + x2 = 12x(1 + x) 56 + x2 = (1 * 12x + x * 12x) 56 + x2 = (12x + 12x2) Solving 56 + x2 = 12x + 12x2 Solving for variable 'x'. Reorder the terms: 56 + -12x + x2 + -12x2 = 12x + 12x2 + -12x + -12x2 Combine like terms: x2 + -12x2 = -11x2 56 + -12x + -11x2 = 12x + 12x2 + -12x + -12x2 Reorder the terms: 56 + -12x + -11x2 = 12x + -12x + 12x2 + -12x2 Combine like terms: 12x + -12x = 0 56 + -12x + -11x2 = 0 + 12x2 + -12x2 56 + -12x + -11x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 56 + -12x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -5.090909091 + 1.090909091x + x2 = 0 Move the constant term to the right: Add '5.090909091' to each side of the equation. -5.090909091 + 1.090909091x + 5.090909091 + x2 = 0 + 5.090909091 Reorder the terms: -5.090909091 + 5.090909091 + 1.090909091x + x2 = 0 + 5.090909091 Combine like terms: -5.090909091 + 5.090909091 = 0.000000000 0.000000000 + 1.090909091x + x2 = 0 + 5.090909091 1.090909091x + x2 = 0 + 5.090909091 Combine like terms: 0 + 5.090909091 = 5.090909091 1.090909091x + x2 = 5.090909091 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 = 5.090909091 + 0.2975206612 Reorder the terms: 0.2975206612 + 1.090909091x + x2 = 5.090909091 + 0.2975206612 Combine like terms: 5.090909091 + 0.2975206612 = 5.3884297522 0.2975206612 + 1.090909091x + x2 = 5.3884297522 Factor a perfect square on the left side: (x + 0.5454545455)(x + 0.5454545455) = 5.3884297522 Calculate the square root of the right side: 2.321299152 Break this problem into two subproblems by setting (x + 0.5454545455) equal to 2.321299152 and -2.321299152.Subproblem 1
x + 0.5454545455 = 2.321299152 Simplifying x + 0.5454545455 = 2.321299152 Reorder the terms: 0.5454545455 + x = 2.321299152 Solving 0.5454545455 + x = 2.321299152 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 = 2.321299152 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + x = 2.321299152 + -0.5454545455 x = 2.321299152 + -0.5454545455 Combine like terms: 2.321299152 + -0.5454545455 = 1.7758446065 x = 1.7758446065 Simplifying x = 1.7758446065Subproblem 2
x + 0.5454545455 = -2.321299152 Simplifying x + 0.5454545455 = -2.321299152 Reorder the terms: 0.5454545455 + x = -2.321299152 Solving 0.5454545455 + x = -2.321299152 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 = -2.321299152 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + x = -2.321299152 + -0.5454545455 x = -2.321299152 + -0.5454545455 Combine like terms: -2.321299152 + -0.5454545455 = -2.8667536975 x = -2.8667536975 Simplifying x = -2.8667536975Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7758446065, -2.8667536975}
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