Can You help me solve these 2 problems? (i need to factor them)?

Question

hi im stuck on the last 2 problems of my summer packet. i\ve searched on google, here, and my algebra book but i just can't figure it out! please help!

1.) x^2 - x - 72 =0

2.) x^2 - 64 =0

i need to factor both of these to find x.

thank you so much! you have no idea how much it means to me!

Answer 1

For number 2:

First things first, always isolate the (x). In this case that means you add 64 to the other side (remembering to add 64 to both sides -- this'll cancel out the original 64, since -64 + 64 = 0) That way you'll be left with x^2=64. Then you'll take the square root of both sides of the equation. The square root of x^2 is x, which means we've finally isolated our variable! The square root of 64 is 8 or -8, which means that x = 8 or -8.

So, in scratchwork, it should look like this:

x^2-64=0

    +64   +64

x^2-(0)=64

x^2=64

(square root of x^2)=(square root of 64)

x=8 x=-8

Answer 2

1.) x^2 - x - 72 = 0

(x - 9) (x + 8)

2.) x^2 - 64 = 0 ← (This is a difference of squares)

(x + 8) (x - 8)

Proficient math skills take practice, so do a few problems each day.

As time goes on, these types of questions become second nature.

Good luck in your studies,

~ Mitch ~