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

May 14, 2016

$x = 4$

Explanation:

Square both sides

$x - 1 = 3$

$\textcolor{b l u e}{\text{Shortcut method}}$

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

$x = 4$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{First principle method}}$

$x - 1 + 1 = 3 + 1$

$x + 0 = 4$

$x = 4$

May 14, 2016

10

Explanation:

$\sqrt{x - 1} = - 3$
squaring both sides
$x - 1 = 9$
$x = 1 + 9$
$x = 10$
valid for negative $\sqrt{x - 1}$