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Simplifying x(11x + 12) = 180 Reorder the terms: x(12 + 11x) = 180 (12 * x + 11x * x) = 180 (12x + 11x2) = 180 Solving 12x + 11x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 12x + 11x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 12x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -16.36363636 + 1.090909091x + x2 = 0 Move the constant term to the right: Add '16.36363636' to each side of the equation. -16.36363636 + 1.090909091x + 16.36363636 + x2 = 0 + 16.36363636 Reorder the terms: -16.36363636 + 16.36363636 + 1.090909091x + x2 = 0 + 16.36363636 Combine like terms: -16.36363636 + 16.36363636 = 0.00000000 0.00000000 + 1.090909091x + x2 = 0 + 16.36363636 1.090909091x + x2 = 0 + 16.36363636 Combine like terms: 0 + 16.36363636 = 16.36363636 1.090909091x + x2 = 16.36363636 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 = 16.36363636 + 0.2975206612 Reorder the terms: 0.2975206612 + 1.090909091x + x2 = 16.36363636 + 0.2975206612 Combine like terms: 16.36363636 + 0.2975206612 = 16.6611570212 0.2975206612 + 1.090909091x + x2 = 16.6611570212 Factor a perfect square on the left side: (x + 0.5454545455)(x + 0.5454545455) = 16.6611570212 Calculate the square root of the right side: 4.081808058 Break this problem into two subproblems by setting (x + 0.5454545455) equal to 4.081808058 and -4.081808058.Subproblem 1
x + 0.5454545455 = 4.081808058 Simplifying x + 0.5454545455 = 4.081808058 Reorder the terms: 0.5454545455 + x = 4.081808058 Solving 0.5454545455 + x = 4.081808058 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 = 4.081808058 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + x = 4.081808058 + -0.5454545455 x = 4.081808058 + -0.5454545455 Combine like terms: 4.081808058 + -0.5454545455 = 3.5363535125 x = 3.5363535125 Simplifying x = 3.5363535125Subproblem 2
x + 0.5454545455 = -4.081808058 Simplifying x + 0.5454545455 = -4.081808058 Reorder the terms: 0.5454545455 + x = -4.081808058 Solving 0.5454545455 + x = -4.081808058 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 = -4.081808058 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + x = -4.081808058 + -0.5454545455 x = -4.081808058 + -0.5454545455 Combine like terms: -4.081808058 + -0.5454545455 = -4.6272626035 x = -4.6272626035 Simplifying x = -4.6272626035Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5363535125, -4.6272626035}
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