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

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Answer 1 · 2017-05-18T12:15:32

$x = - 6, 5$

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 $5$ .

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