Solve by factoring or finding square roots
x^2-1=0

{1,-1}

Step-by-step explanation:

Let's do both!

Factoring!

x^2-1 is a difference of squares.

The formula for factoring a difference of squares is: u^2-v^2=(u-v)(u+v).

So the factored form of x^2-1 is (x-1)(x+1).

So we want to solve the equation x^2-1=0 which is equivalent to solving

(x-1)(x+1)=0.

If you have A*B=0 then either A=0 or B=0.

So in our case we have x-1=0 or x+1=0.

Now we just solve the equations.

x-1=0 can be solved by adding 1 on both sides giving us x=1.

x+1=0 can be solved by subtracting 1 on both sides giving us x=-1.

Square root!

When you want to use square roots, you have to have a perfect square containing the variables and a constant.  We have that here.

We have x^2-1=0 which is equivalent to x^2=1.  You could get this last equation by adding one on both sides of x^2-1=0.

Anyway, once you have the square part equals the constant, all you have to do is square root both sides to get rid of the square on the variable part.

 It leads to two answers because .

the answer is 24

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x