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

May 18, 2017

$x = - 6 , 5$

#### Explanation:

We have: $y + 30 = {x}^{2} + x$

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

$R i g h t a r r o w y = {x}^{2} + x - 30$

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

$R i g h t a r r o w y = 0$

$R i g h t a r r o w {x}^{2} + x - 30 = 0$

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

$R i g h t a r r o w {x}^{2} + 6 x - 5 x - 30 = 0$

$R i g h t a r r o w x \left(x + 6\right) - 5 \left(x + 6\right) = 0$

$R i g h t a r r o w \left(x + 6\right) \left(x - 5\right) = 0$

Using the null factor law:

$R i g h t a r r o w x + 6 = 0 , x - 5 = 0$

$\therefore x = - 6 , 5$

Therefore, the $x$- intercepts of the graph of $y + 30 = {x}^{2} + x$ are $- 6$ and $5$.