# How do you solve #sqrt(x+5) + sqrt(x+15) = sqrt(9x+40)#?

##### 1 Answer

Square, rearrange and square again to get a quadratic, one of whose roots is a valid solution:

#### Explanation:

Note that both sides are non-negative, being the sums of non-negative square roots. So squaring both sides will not introduce spurious solutions.

So square both sides to get:

Subtract

**Note that a valid solution will require #7x + 20 >= 0#.**

Square both sides (which may introduce extraneous solutions with

Subtract the right hand side from the left to get:

Divide through by

Solve using the quadratic formula: