Question 81000
QUESTION:


(x-1)^2=5



SOLUTION:



At first expand the expression using the identity (a-b)^2 = a^2 - 2ab + b^2 as follows............



(X-1)^2 = 5




==> x^2 - 2x + 1 = 5




subtract 5 from both sides





==> x^2 - 2x + 1 - 5 = 5 - 5 




==> x^2 - 2x - 5 = 0




This is a quadratic equation so we can solve it using quadratic formula.




comparing with the standard equation, ax^2 + bx + c = 0, we have,



a = 1  b = -2  and c = -5



So solution is given by,




{{{x = (-(-2) +- sqrt( (-2)^2-4*1*(-5) ))/(2*1) }}} 




{{{x = (2 +- sqrt( 4+ 20 ))/2 }}} 




{{{x = (2 +- sqrt( 24))/2 }}} 





{{{x = (2 +- 4.9)/2 }}}




==> x = (2 + 4.9)/2  or x = (2-4.9)/2




==>  x = 6.9/2     or  x = -2.9/2




==> x = 3.45  or  x = -1.45




To check your solution, substitute any of these values for x in the given equation, you will get tha answer 5, which is in the right hand side.




Hope you found this explanation useful.



Regards.



Praseena.