Question

What is the solution to the equation below? √ x-5 = x-11

Answer 1

Answer:

x= 14

Step-by-step explanation:

sqrt( x-5) = x-11

Square each side

(sqrt( x-5))^2 = (x-11)^2

x-5 = x^2 - 22x +121

Subtract (x-5) from each side

x-5-x+5 = x^2 -22x +121 -x+5

0 = x^2 -23x +126

Factor

0 = ( x-14) ( x-9)

Using the zero product property

x-14 = 0   x-9=0

x=14 x=9

Check the solutions

sqrt( x-5) = x-11

sqrt( 14-5) = 14-11

sqrt(9) = 3

3=3

solution

sqrt( x-5) = x-11

sqrt(9-5) = 9-11

sqrt(4) =-2

2 = -2

not a solution