# How do you solve sqrt(x+10)=-3?

May 2, 2016

This has no solution.

#### Explanation:

The left hand side denotes the principal square root of $x + 10$.

If $x + 10 \ge 0$ then this is the non-negative square root, so cannot be equal to $- 3$.

If $x + 10 < 0$ then this is the pure imaginary square root on the positive part of the imaginary axis and cannot be equal to $- 3$ either.

Note that the normal way to attempt to solve such an equation would be to start by squaring both sides, giving:

$x + 10 = 9$

and hence:

$x = - 1$

Then the left hand side of the original equation is:

$\sqrt{x + 10} = \sqrt{- 1 + 10} = \sqrt{9} = 3 \ne - 3$