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

1 Answer
May 18, 2017

Answer:

#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#.