Question

How do I find the root of x^2 - 36 = 0 by factoring?

Answer 1

x = -6 and x = 6

Step-by-step explanation:

If we have the difference of two perfect squares, we can factor the expression as:

`a^2-b^2=(a+b)(a-b)`

In this case, x² and 36 are perfect squares, so, we can factorize the expression as:

`\begin{gathered} x^2-36=0 \\ (x+6)(x-6)=0_{} \end{gathered}`

Now, if the multiplication of two numbers is 0, one of the numbers is equal to zero. It means that the possible solutions for the equation are:

x + 6 = 0

or

x - 6 = 0

So, solving for x, we get:

x + 6 = 0

x + 6 - 6 = 0 - 6

x = - 6

or

x - 6 = 0

x - 6 + 6 = 0 + 6

x = 6

Therefore, the roots of x² - 36 = 0 are:

x = -6 and x = 6