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Example 8 - Find roots of 5x2 - 6x - 2 = 0 by completing sq - Solving by completing square

  1. Chapter 4 Class 10 Quadratic Equations
  2. Serial order wise
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Example 8 Find the roots of the equation 5x2 โ€“ 6x โ€“ 2 = 0 by the method of completing the square. 5x2 โ€“ 6x โ€“ 2 = 0 Dividing by 5 (5๐‘ฅ2 โˆ’ 6๐‘ฅ โˆ’ 2)/5=0/5 5๐‘ฅ2/5โˆ’6๐‘ฅ/5โˆ’2/5=0 x2 โ€“ 6๐‘ฅ/5โˆ’2/5=0 We know that (a โ€“ b)2 = a2 โ€“ 2ab + b2 Here, a = x & โ€“ 2ab = (โˆ’ 6๐‘ฅ)/5 โ€“ 2xb = (โˆ’ 6๐‘ฅ)/5 โ€“ 2b = (โˆ’ 6)/5 b = (โˆ’6)/(5 ร— (โˆ’2)) b = 3/5 Now, in our equation x2 โ€“ 6๐‘ฅ/5โˆ’2/5=0 Adding and subtracting (3/5)^2 x2 โ€“ 6๐‘ฅ/5โˆ’2/5+(3/5)^2โˆ’(3/5)^2=0 x2 โ€“ 6๐‘ฅ/5+(3/5)^2โˆ’2/5โˆ’(3/5)^2=0 (๐‘ฅโˆ’3/5)^2โˆ’2/5โˆ’(3/5)^2=0 (๐‘ฅโˆ’3/5)^2=(3/5)^2+2/5 (๐‘ฅโˆ’3/5)^2=9/25+2/5 (๐‘ฅโˆ’3/5)^2=(9 + 2(5))/25 (๐‘ฅโˆ’3/5)^2=(9 +10)/25 (๐‘ฅโˆ’3/5)^2=19/25 (๐‘ฅโˆ’3/5)^2=(โˆš19)^2/5^2 Cancelling squares both sides ๐‘ฅโˆ’3/5 = ยฑ โˆš19/5 ๐‘ฅโˆ’3/5 = ยฑ โˆš19/5 Solving So, x = (โˆš(19 )+ 3)/5 and x = (โˆ’ โˆš19 + 3)/5 are the roots of the equation .

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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