Solve using the Square Root Property (x-5)^2-2(x-5)-24=0

(x-5)2-2(x-5)-24=0
Factor the left side of the equation.
Let u=x-5. Substitute u for all occurrences of x-5.
u2-2u-24
Factor u2-2u-24 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -24 and whose sum is -2.
-6,4
Write the factored form using these integers.
(u-6)(u+4)
(u-6)(u+4)
Replace all occurrences of u with x-5.
(x-5-6)(x-5+4)
Simplify.
Subtract 6 from -5.
(x-11)(x-5+4)
(x-11)(x-1)
(x-11)(x-1)
Replace the left side with the factored expression.
(x-11)(x-1)=0
(x-11)(x-1)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x-11=0
x-1=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
x-11=0
Add 11 to both sides of the equation.
x=11
x=11
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
x-1=0
Add 1 to both sides of the equation.
x=1
x=1
The final solution is all the values that make (x-11)(x-1)=0 true.
x=11,1
Solve using the Square Root Property (x-5)^2-2(x-5)-24=0