i dont know how to solve this. Help please! Nov 4 | Mathalina from Louisville, KY | 1 Answer | 0 Votes Mark favorite Subscribe Comment
Are we supposed to interpret this as: A. (6/x) + (4/x) +2 = 1 or B. (6/x) + [4/(x+2)} = 1? If A., then x = -10 If B, then x = -2*[(√7) - 2] or x = 2*[(√7) + 2] Nov 4 | William S. Comment Comments It is supposed to be interpreted as B. 6 + 4 = 1 x x+2 I still don't understand the process of getting to those numbers. I am supposed to a. solve by completing the square b. solve using the quadratic formula Nov 4 | Mathalina from Louisville, KY OK, so the correct interpretation is B (6/x) + [4/(x+2)} = 1 Complete the square method: Multiply by x 6 =[4x/(x+2)] = x Multiply by (x + 2) (6)*(x + 2) +4x = (x)*(x + 2) 6x + 12 +4x = x^{2} +2x 6x + 12 + 4x = x^{2} = 2x Therefore x^{2} - 8x = 12 or x^{2} - 8x - 12 = 0 [Let's call this Eq. (1)] Take half the x coefficient, square it, and add to both sides x^{2} - 8x + 16 = 12 + 16 (x - 4)^{2} + 16 = 28 (x - 4)^{2} = 28 from which x = -2*[(√7) - 2] or x = 2*[(√7) + 2] B. Quadratic formula x = [-b ±(b^{2} - 4ac)^{1/2}]/2a Going back to Eq. (1) a = 1, b = -8, c = -12 x = {8 ± [64 - (4)(1)(-12)]^{1/2}}/2(1) = {[8 ± √(112)]}/2} From which x = -2*[(√7) - 2] or x = 2*[(√7) + 2] I hope this helps Mathalina! Nov 5 | William S. Comment
It is supposed to be interpreted as B. 6 + 4 = 1 x x+2 I still don't understand the process of getting to those numbers. I am supposed to a. solve by completing the square b. solve using the quadratic formula Nov 4 | Mathalina from Louisville, KY
OK, so the correct interpretation is B (6/x) + [4/(x+2)} = 1 Complete the square method: Multiply by x 6 =[4x/(x+2)] = x Multiply by (x + 2) (6)*(x + 2) +4x = (x)*(x + 2) 6x + 12 +4x = x^{2} +2x 6x + 12 + 4x = x^{2} = 2x Therefore x^{2} - 8x = 12 or x^{2} - 8x - 12 = 0 [Let's call this Eq. (1)] Take half the x coefficient, square it, and add to both sides x^{2} - 8x + 16 = 12 + 16 (x - 4)^{2} + 16 = 28 (x - 4)^{2} = 28 from which x = -2*[(√7) - 2] or x = 2*[(√7) + 2] B. Quadratic formula x = [-b ±(b^{2} - 4ac)^{1/2}]/2a Going back to Eq. (1) a = 1, b = -8, c = -12 x = {8 ± [64 - (4)(1)(-12)]^{1/2}}/2(1) = {[8 ± √(112)]}/2} From which x = -2*[(√7) - 2] or x = 2*[(√7) + 2] I hope this helps Mathalina! Nov 5 | William S.
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