Question

How do you solve `49x^2 - 64 = 0`?

Answer 1

`x= 8/7 or x= -8/7`

Explanation:

`49x^2-64=0 or (7x)^2-(8)^2=0 or (7x+8)(7x-8)=0 :. (7x-8)=0 or (7x+8)=0 :.x= 8/7 or x= -8/7`[Ans]

Answer 2

`x = =8/7 or x = -8/7`

Explanation:

Usually we make a quadratic equal to 0 to be able to solve it.
This is an exception, where we can use the normal method of x on one side and the numbers on the other.

`49x^2 = 64`

`x^2 = 64/49 " find the square root of both sides"`

`x = +-sqrt(64/49)`

`x = =8/7 or x = -8/7`

However, we can also use the factorising method:

`49x^2 - 64 = 0 " the difference of two squares"`

`(7x + 8)(7x - 8)=0`

`x = -8/7 or x = 8/7`