(x-5)2-2(x-5)-24=0

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)

Add -5 and 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.

x-11=0

Add 11 to both sides of the equation.

x=11

x=11

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