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Simplifying 5x + 5 + 8x(12x + 6) = 3675 Reorder the terms: 5x + 5 + 8x(6 + 12x) = 3675 5x + 5 + (6 * 8x + 12x * 8x) = 3675 5x + 5 + (48x + 96x2) = 3675 Reorder the terms: 5 + 5x + 48x + 96x2 = 3675 Combine like terms: 5x + 48x = 53x 5 + 53x + 96x2 = 3675 Solving 5 + 53x + 96x2 = 3675 Solving for variable 'x'. Reorder the terms: 5 + -3675 + 53x + 96x2 = 3675 + -3675 Combine like terms: 5 + -3675 = -3670 -3670 + 53x + 96x2 = 3675 + -3675 Combine like terms: 3675 + -3675 = 0 -3670 + 53x + 96x2 = 0 Begin completing the square. Divide all terms by 96 the coefficient of the squared term: Divide each side by '96'. -38.22916667 + 0.5520833333x + x2 = 0 Move the constant term to the right: Add '38.22916667' to each side of the equation. -38.22916667 + 0.5520833333x + 38.22916667 + x2 = 0 + 38.22916667 Reorder the terms: -38.22916667 + 38.22916667 + 0.5520833333x + x2 = 0 + 38.22916667 Combine like terms: -38.22916667 + 38.22916667 = 0.00000000 0.00000000 + 0.5520833333x + x2 = 0 + 38.22916667 0.5520833333x + x2 = 0 + 38.22916667 Combine like terms: 0 + 38.22916667 = 38.22916667 0.5520833333x + x2 = 38.22916667 The x term is 0.5520833333x. Take half its coefficient (0.2760416667). Square it (0.07619900175) and add it to both sides. Add '0.07619900175' to each side of the equation. 0.5520833333x + 0.07619900175 + x2 = 38.22916667 + 0.07619900175 Reorder the terms: 0.07619900175 + 0.5520833333x + x2 = 38.22916667 + 0.07619900175 Combine like terms: 38.22916667 + 0.07619900175 = 38.30536567175 0.07619900175 + 0.5520833333x + x2 = 38.30536567175 Factor a perfect square on the left side: (x + 0.2760416667)(x + 0.2760416667) = 38.30536567175 Calculate the square root of the right side: 6.189132869 Break this problem into two subproblems by setting (x + 0.2760416667) equal to 6.189132869 and -6.189132869.Subproblem 1
x + 0.2760416667 = 6.189132869 Simplifying x + 0.2760416667 = 6.189132869 Reorder the terms: 0.2760416667 + x = 6.189132869 Solving 0.2760416667 + x = 6.189132869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2760416667' to each side of the equation. 0.2760416667 + -0.2760416667 + x = 6.189132869 + -0.2760416667 Combine like terms: 0.2760416667 + -0.2760416667 = 0.0000000000 0.0000000000 + x = 6.189132869 + -0.2760416667 x = 6.189132869 + -0.2760416667 Combine like terms: 6.189132869 + -0.2760416667 = 5.9130912023 x = 5.9130912023 Simplifying x = 5.9130912023Subproblem 2
x + 0.2760416667 = -6.189132869 Simplifying x + 0.2760416667 = -6.189132869 Reorder the terms: 0.2760416667 + x = -6.189132869 Solving 0.2760416667 + x = -6.189132869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2760416667' to each side of the equation. 0.2760416667 + -0.2760416667 + x = -6.189132869 + -0.2760416667 Combine like terms: 0.2760416667 + -0.2760416667 = 0.0000000000 0.0000000000 + x = -6.189132869 + -0.2760416667 x = -6.189132869 + -0.2760416667 Combine like terms: -6.189132869 + -0.2760416667 = -6.4651745357 x = -6.4651745357 Simplifying x = -6.4651745357Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.9130912023, -6.4651745357}
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