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Simplifying (x + 66)(x + 47) = 79 Reorder the terms: (66 + x)(x + 47) = 79 Reorder the terms: (66 + x)(47 + x) = 79 Multiply (66 + x) * (47 + x) (66(47 + x) + x(47 + x)) = 79 ((47 * 66 + x * 66) + x(47 + x)) = 79 ((3102 + 66x) + x(47 + x)) = 79 (3102 + 66x + (47 * x + x * x)) = 79 (3102 + 66x + (47x + x2)) = 79 Combine like terms: 66x + 47x = 113x (3102 + 113x + x2) = 79 Solving 3102 + 113x + x2 = 79 Solving for variable 'x'. Reorder the terms: 3102 + -79 + 113x + x2 = 79 + -79 Combine like terms: 3102 + -79 = 3023 3023 + 113x + x2 = 79 + -79 Combine like terms: 79 + -79 = 0 3023 + 113x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3023' to each side of the equation. 3023 + 113x + -3023 + x2 = 0 + -3023 Reorder the terms: 3023 + -3023 + 113x + x2 = 0 + -3023 Combine like terms: 3023 + -3023 = 0 0 + 113x + x2 = 0 + -3023 113x + x2 = 0 + -3023 Combine like terms: 0 + -3023 = -3023 113x + x2 = -3023 The x term is 113x. Take half its coefficient (56.5). Square it (3192.25) and add it to both sides. Add '3192.25' to each side of the equation. 113x + 3192.25 + x2 = -3023 + 3192.25 Reorder the terms: 3192.25 + 113x + x2 = -3023 + 3192.25 Combine like terms: -3023 + 3192.25 = 169.25 3192.25 + 113x + x2 = 169.25 Factor a perfect square on the left side: (x + 56.5)(x + 56.5) = 169.25 Calculate the square root of the right side: 13.009611831 Break this problem into two subproblems by setting (x + 56.5) equal to 13.009611831 and -13.009611831.Subproblem 1
x + 56.5 = 13.009611831 Simplifying x + 56.5 = 13.009611831 Reorder the terms: 56.5 + x = 13.009611831 Solving 56.5 + x = 13.009611831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-56.5' to each side of the equation. 56.5 + -56.5 + x = 13.009611831 + -56.5 Combine like terms: 56.5 + -56.5 = 0.0 0.0 + x = 13.009611831 + -56.5 x = 13.009611831 + -56.5 Combine like terms: 13.009611831 + -56.5 = -43.490388169 x = -43.490388169 Simplifying x = -43.490388169Subproblem 2
x + 56.5 = -13.009611831 Simplifying x + 56.5 = -13.009611831 Reorder the terms: 56.5 + x = -13.009611831 Solving 56.5 + x = -13.009611831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-56.5' to each side of the equation. 56.5 + -56.5 + x = -13.009611831 + -56.5 Combine like terms: 56.5 + -56.5 = 0.0 0.0 + x = -13.009611831 + -56.5 x = -13.009611831 + -56.5 Combine like terms: -13.009611831 + -56.5 = -69.509611831 x = -69.509611831 Simplifying x = -69.509611831Solution
The solution to the problem is based on the solutions from the subproblems. x = {-43.490388169, -69.509611831}
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