Solving square roots

Question

26 + 3 root 4y-5 = 2 root 4y-5 + 7

Answer 1

26+3sqr(4y-5) = 2sqr(4y-5)+7

Let x=sqr(4y-5)

26+3x=2x+7, subtract 2x from both sides, subtract 26 from both sides

x=-19

sqr(4y-5) = -19

There's a problem, as the square root of any number is always positive

-19 is negative. There is no solution.

I'm assuming by root 4y-5 you mean the square root of (4y-5). If so there's no solution.

Even if you meant square root of 4y and then subtract 5

then let x=square root of 4y to

get

26+3x-5 = 2x-5+7

x=2-21=-19. then there's still no solution as x=square root of 4y

as the square root of 4y can't be negative

You could square both sides and eliminate the negative sign, but that introduces an extraneous solution that's not in the original problem. If you meant the negative square root of 4y-5

Then the square root of 4y-5=19

squared = 361

4y-5=361

4y=361+5 = 366

y=366/4=91.5

check the answer 4y-5= 4(91.5)-5=366-5=361. square root of 361=19

26-3(19)=-2(19)+7

26-57 =-38+7

-31 = -31