Question

What are the x-intercept(s) of the graph of `y + 30 = x^2 + x`?

Answer 1

`x = - 6, 5`

Explanation:

We have: `y + 30 = x^(2) + x`

Let's express the equation in terms of `y`:

`Rightarrow y = x^(2) + x - 30`

Now that `y` is a function of `x`, we can set it equal to zero to find the `x`- intercepts:

`Rightarrow y = 0`

`Rightarrow x^(2) + x - 30 = 0`

Then, let's factorise the equation using the "middle-term break":

`Rightarrow x^(2) + 6 x - 5 x - 30 = 0`

`Rightarrow x (x + 6) - 5 (x + 6) = 0`

`Rightarrow (x + 6)(x - 5) = 0`

Using the null factor law:

`Rightarrow x + 6 = 0, x - 5 = 0`

`therefore x = - 6, 5`

Therefore, the `x`- intercepts of the graph of `y + 30 = x^(2) + x` are `- 6` and `5`.