Solve the equation. Write all proposed solutions.

Question

(Square root)   /2a-8    +8=a

 

2a-8 is the only thing under radical. Part im confused about is that answer rquires a larger value and smaller value answer

Answer 1

Starting with Andy's fourth line:

0 = a² - 18a + 72

0 = (a - 6)(a - 12)

{6, 12}

 

Using 6 results in the right side being negative. It is discarded.

Answer 2

sqrt(2A-8) + 8 = A

 

sqrt(2A-8) = A - 8

 

2A - 8 = A^2 - 16A + 64

 

0 = A^2 - 18A + 72

 

A = [18 +or- sqrt (  324 - 4*72) ]/2

 

A = [18 +or- sqrt( 324 - 288) ] /2

 

A = [ 18 +or- sqrt( 36) ] /2

 

A = [ 18 +or- 6]/2

 

A = (18+6)/2 = 24/2 = 12

 

or

 

A = (18-6)/2 = 12/2 = 6

 

 

Both answers MUST be checked.

A=12 works. A=6 does not.