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

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Answer 1 · 2016-05-02T14:45:00

This has no solution.

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

If $x+10 >= 0$ 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:

$sqrt(x+10) = sqrt(-1+10) = sqrt(9) = 3 != -3$

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