What is the solution to the equation sqrt w^2+7w-39 = sqrt 10w+1 ?

Square both sides
w^2+7w-39=10w+1
minus (10w+1) both sides
w^2-3w-40=0
factor
what 2 numbers multiply to get -40 and add to get -3
-8 and 5
(w-8)(w+5)=0

set equal to 0

w-8=0
w=0

w+5=0
w=-5

we need to test in the original for extraneious solutions
for x=-5, we get √-49=√-49 which is undefined since you can't do square roots of negatives

w=8 is da soltuion

Ithink the correct answer is d.