Verified answer

√(3x-5)+2=-3

√(3x-5) = - 3 - 2

√(3x-5)^2 = (- 5)^2

 3x - 5 = 25

3x = 25 + 5

3x = 30

 x =10

checking your answer..

√[3(10) - 5)] + 2 = - 3

 √(30 - 5) + 2 = - 3

 √(25) + 2 = - 3

 5 + 2 = - 3

 7 ≠ - 3, it is not a solution of the equation since it is not equal to each other..//

7 is the result

√(3x - 5) + 2 = -3

√(3x - 5) = -5

3x - 5 = 25

3x = 30

x = 10

x = -5/3 (i +1)  obviously there is not a Real solution

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√(3x-5)+2=-3

√(3x-5) = -5

multiply both sides by √i

√i(3x-5) = -5√i

square both sides

i(3x-5) = -5(-1)

divide by i

3x -5 = 5/i

x = 1/3(5/i  -5)

multiply 1/i by (i/i)

x = 5/3 (-i -1)

x = -5/3 (i +1)

√ (3x - 5) cannot be (-ve)

If we include complex numbers and non-principal roots, we get:

sqrt(3x - 5) + 2 = -3

sqrt(3x - 5) = -5

3x - 5 = (-5)^2

3x - 5 = 25

3x = 30

x = 10

If we only include principal (i.e., positive) roots, then there's no solution.

sum of 2 positives cannot be a negative !!!

√(3x-5)+2=-3  

subtract 2 from both sides

√(3x-5)  = -5  

there is no square root, that is equal to -5 , unless you are working with 

complex numbers. 

Don't see anything wrong with what you did. Square roots have +/- values and using -5 for the square root of 3(10)-5 = 25 makes it work out.

Plug 10 into the function and you'll find that you get 7=-3

You can also try graphing the function in desmos to see why there isn't a solution.