# Solve the following: ((x-9)^.5 ) + 1 = x^.5I''m using the ^ to indicate take the item before to the power after the ^.   This means to take (x-9) to the 1/2 power which means to take the square...

Solve the following:

((x-9)^.5 ) + 1 = x^.5

I''m using the ^ to indicate take the item before to the power after the ^.   This means to take (x-9) to the 1/2 power which means to take the square root of (x-9).  Tks, John

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation to be solved is ((x-9)^0.5 ) + 1 = x^0.5

((x-9)^0.5 ) + 1 = x^0.5

square both the sides

=> [((x-9)^0.5 ) + 1]^2 = [x^0.5]^2

=> (x - 9) + 1 + 2*(x-9)^0.5 = x

=> 2*(x-9)^0.5 - 8 = 0

=> (x-9)^0.5 = 4

square both the sides

=> x - 9 = 16

=> x = 25

The required solution of the equation is x = 25

samir-aguiar | Student, Undergraduate | eNotes Newbie

Posted on

Consider srqrt(x) as the square root of x.

We have:

sqrt(x-9) + 1 = sqrt(x) :: taking both side to the power of 2

[sqrt(x-9) + 1]^2 = [sqrt(x)]^2

(x-9) + 2*[sqrt(x-9)*1] + 1 = x :: subtracting x on both sides

2*[sqrt(x-9)] - 8 = 0 :: adding 8 to both sides and dividing by 2

sqrt(x-9) = 4 :: taking both sides to the power of 2

x-9 = 16 :: adding 9 to both sides

x = 25

hope that helps =)