How do you evaluate #\sqrt { x + 7} - x = 5#?

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Answer 1 · 2016-12-11T10:35:24

#x=-3# or #x=-6#

#sqrt(x+7)-x=5#

#hArrsqrt(x+7)=5+x#

Squaring each side we get

#x+7=(5+x)^2=25+10x+x^2#

or #x^2+10x-x+25-7=0#

or #x^2+9x+18=0$

or #x^2+6x+3x+18=0#

or #x(x+6)+3(x+6)=0#

or #(x+3)(x+6)=0#

i.e. either #x+3=0# or #x+6=0#

i.e. #x=-3# or #x=-6#