How do you solve #15- 2\sqrt { x + 3} = 7#?

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Answer 1 · 2017-08-01T21:29:35

See below.

Rearranging the common parts together,

#15- 2\sqrt { x + 3} = 7#

#8= 2\sqrt { x + 3}#

#4= \sqrt { x + 3}#

Squaring both sides,

#16=x+3#

#x=13#

We must make sure this is not extraneous.

#sqrt(13+3)=sqrt(16>0)#, so this solution is real. Thus, our only real solution is #x=13#.

Answer 2 · 2017-08-01T21:34:53

#x=13#

Refer to the explanation for the process.

Solve:

#15-2sqrt(x+3)=7#

Subtract #15# from both sides.

#-2sqrt(x+3)=7-15#

Simplify.

#-2sqrt(x+3)=-8#

Square both sides.

#(-2sqrt(x+3))^2=(-8)^2#

Simplify.

#4(x+3)=64#

Divide both sides by #4#.

#x+3=64/4#

Simplify.

#x+3=16#

Subtract #3# from both sides.

#x=16-3#

Simplify.

#x=13#