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 $sqrt(x-1)$

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