# How do you solve #2sqrt(x+2)-3=7#?

##### 1 Answer

#### Answer:

#### Explanation:

Given:

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

Add

#2 sqrt(x+2) = 10#

Divide both sides by

#sqrt(x+2) = 5#

Square both sides (noting that this can introduce spurious solutions) to get:

#x+2 = 25#

Subtract

#x = 23#

Check:

#2 sqrt(23+2) - 3 = 2 sqrt(25)-3 = (2*5)-3 = 10 - 3 = 7#

**Notes**

Why the concern about squaring both sides of the equation?

When you square both sides of an equation, solutions of the resulting equation may not be solutions of the original, due to having different signs. The function

For example, if you had:

#sqrt(x+2) = -5#

then squaring both sides would give:

#x+2 = 25#

and hence:

#x=23#

but we have