Solve the eq. x²-10x-2=0 by completing sq. Method

1.	Solve the eq. x²-10x-2=0 by completing sq. Method
Answer» We have{tex}x^2 - 10x\xa0- 2 = 0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}x^2 - 10x\xa0= 2{/tex}{tex}\\Rightarrow{/tex}\xa0x2 - 2 {tex}\\times{/tex}\xa0x {tex}\\times{/tex}\xa05 + 52 = 2 + 52 [adding 52 on both sides]{tex}\\Rightarrow{/tex}\xa0{tex}(x\xa0- 5)^2 = (2 + 25) = 27{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}x\xa0- 5 ={/tex}{tex}\\pm \\sqrt { 27 } = \\pm 3 \\sqrt { 3 }{/tex} [taking square root on both sides]{tex}\\Rightarrow{/tex}\xa0{tex}x -\xa05 ={/tex}{tex}3 \\sqrt { 3 }{/tex} or x\xa0- 5 = -{tex}3 \\sqrt { 3 }{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}x\xa0= (5 +{/tex}{tex}3 \\sqrt { 3 }{/tex}) or x\xa0= (5 -\xa0{tex}3 \\sqrt { 3 }{/tex}\xa0).Hence, (5 + {tex}3 \\sqrt { 3 }{/tex}) and (5 -{tex}3 \\sqrt { 3 }{/tex}) are the roots of the given equation.

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