How do you solve the equation #x^2-8x=-9# by completing the square?

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Answer 1 · 2017-03-19T05:33:54

#x=6.64575131 or x=1.35424868#

#color(red)(Commenci ng)# #color(red)(compl e ti ng)# #color(red)(the)# #color(red)(squ are)# #color(red)(method)# #color(red)(now,)#

1) Know the formula for the perfect quadratic square, which is,

#(ax+-b)^2 = ax^2+-2abx+b^2#

2) Figure out your #a and b# values,

#a=# coefficient of #x^2#, which is #1#.
#color(red)(b=(-8)/(2(1)) = -4)#

3) Add #color(red)(b^2)# on both sides of the equation, giving you an overall net of 0, hence not affecting the result of the equation,

#x^2-8x+color(red)((-4)^2)=-9+color(red)((-4)^2)#
#(x-4)^2=7#

4) Square root both sides,

#x-4=+-sqrt(7)#

5) Add #4# on both sides,

#x=+-sqrt7+4#

6) Calculate the two values of #x#,

#x=6.64575131 or x=1.35424868#