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#