How do you solve #sqrt(x-1)=-3#?

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Answer 1 · 2016-05-14T15:47:23

#x=4#

Square both sides

#x-1=3#

#color(blue)("Shortcut method")#

Move the -1 to the other side of the equals
#x=3+1#

#x=4#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("First principle method")#

Add 1 to both sides

#x-1+1=3+1#

#x+0=4#

#x=4#

Answer 2 · 2016-05-14T15:59:24

10

#sqrt(x-1)=-3#
squaring both sides
#x-1=9#
#x=1+9#
#x=10#
valid for negative #sqrt(x-1)#