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Simplifying (11x + 2)(8x + 20) = x Reorder the terms: (2 + 11x)(8x + 20) = x Reorder the terms: (2 + 11x)(20 + 8x) = x Multiply (2 + 11x) * (20 + 8x) (2(20 + 8x) + 11x * (20 + 8x)) = x ((20 * 2 + 8x * 2) + 11x * (20 + 8x)) = x ((40 + 16x) + 11x * (20 + 8x)) = x (40 + 16x + (20 * 11x + 8x * 11x)) = x (40 + 16x + (220x + 88x2)) = x Combine like terms: 16x + 220x = 236x (40 + 236x + 88x2) = x Solving 40 + 236x + 88x2 = x Solving for variable 'x'. Reorder the terms: 40 + 236x + -1x + 88x2 = x + -1x Combine like terms: 236x + -1x = 235x 40 + 235x + 88x2 = x + -1x Combine like terms: x + -1x = 0 40 + 235x + 88x2 = 0 Begin completing the square. Divide all terms by 88 the coefficient of the squared term: Divide each side by '88'. 0.4545454545 + 2.670454545x + x2 = 0 Move the constant term to the right: Add '-0.4545454545' to each side of the equation. 0.4545454545 + 2.670454545x + -0.4545454545 + x2 = 0 + -0.4545454545 Reorder the terms: 0.4545454545 + -0.4545454545 + 2.670454545x + x2 = 0 + -0.4545454545 Combine like terms: 0.4545454545 + -0.4545454545 = 0.0000000000 0.0000000000 + 2.670454545x + x2 = 0 + -0.4545454545 2.670454545x + x2 = 0 + -0.4545454545 Combine like terms: 0 + -0.4545454545 = -0.4545454545 2.670454545x + x2 = -0.4545454545 The x term is 2.670454545x. Take half its coefficient (1.335227273). Square it (1.782831871) and add it to both sides. Add '1.782831871' to each side of the equation. 2.670454545x + 1.782831871 + x2 = -0.4545454545 + 1.782831871 Reorder the terms: 1.782831871 + 2.670454545x + x2 = -0.4545454545 + 1.782831871 Combine like terms: -0.4545454545 + 1.782831871 = 1.3282864165 1.782831871 + 2.670454545x + x2 = 1.3282864165 Factor a perfect square on the left side: (x + 1.335227273)(x + 1.335227273) = 1.3282864165 Calculate the square root of the right side: 1.152513087 Break this problem into two subproblems by setting (x + 1.335227273) equal to 1.152513087 and -1.152513087.Subproblem 1
x + 1.335227273 = 1.152513087 Simplifying x + 1.335227273 = 1.152513087 Reorder the terms: 1.335227273 + x = 1.152513087 Solving 1.335227273 + x = 1.152513087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.335227273' to each side of the equation. 1.335227273 + -1.335227273 + x = 1.152513087 + -1.335227273 Combine like terms: 1.335227273 + -1.335227273 = 0.000000000 0.000000000 + x = 1.152513087 + -1.335227273 x = 1.152513087 + -1.335227273 Combine like terms: 1.152513087 + -1.335227273 = -0.182714186 x = -0.182714186 Simplifying x = -0.182714186Subproblem 2
x + 1.335227273 = -1.152513087 Simplifying x + 1.335227273 = -1.152513087 Reorder the terms: 1.335227273 + x = -1.152513087 Solving 1.335227273 + x = -1.152513087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.335227273' to each side of the equation. 1.335227273 + -1.335227273 + x = -1.152513087 + -1.335227273 Combine like terms: 1.335227273 + -1.335227273 = 0.000000000 0.000000000 + x = -1.152513087 + -1.335227273 x = -1.152513087 + -1.335227273 Combine like terms: -1.152513087 + -1.335227273 = -2.48774036 x = -2.48774036 Simplifying x = -2.48774036Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.182714186, -2.48774036}
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