Question

How do you solve `36x^2 - 25 = 0`?

Answer 1

`x = -5/6 or x = 5/6`

Explanation:

For quadratic equations, there are 3 methods of solving them:

• factorise if possible
• completing the square
• quadratic formula

This equation can be factorised as the difference of two squares.

`36x^2 - 25 =0`
`(6x + 5)(6x - 5)=0`

Let each factor in turn be equal to 0.

If `6x + 5 = 0, " or " if 6x - 5 = 0`
`6x = -5 " " 6x = 5`
`x = -5/6 " " x = 5/6`

There are two solutions as we expect for a quadratic.