Question

How do you solve `x ^ { 2} - 24x + 144= 36`?

Answer 1

Factor or quadratic formula. Factoring works fine in this example. As a result, you get `6` and `18`.

Explanation:

So solving a quadratic equation implies that we are solving for `x` - the zeros/roots/solutions.

There are two main ways to do this:

1. Factoring (from standard).
2. Quadratic formula (from standard).

If `x^2 - 24x + 144 = 36`, then we would have to bring over `36` to the "other side", and then equate the equation to the `0`.

`x^2 - 24x + 144 = 36`

`x^2 - 24x + 144 - 36 = 0`

`x^2 - 24x + 108 = 0`

Now, this is a simple trinomial. So let's see if we can factor it normally: "what two numbers added equals `b`, and multiplied equals #ac?"

We see that `-18` and `-6` works perfectly. Therefore, we get:

`(x-6)(x-18) = 0`

Isolate the `x` in their respective brackets and the solutions are `6` and `18`.

Hope this helps :)