Question

Can someone help me with the rest of this?

Here is the question: Having survived the meteor impact, thanks to some last-minute evasive maneuvers, the Mathonauts now set their sights on their Interstellar Headquarters. The Interstellar Headquarters orbits the Earth based on the equation y2 + x2 = 40,000. Using the original trajectory of the ship and complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path.

Answer 1

My original equation is y = 5x + 3

Answer 2

Here's are my steps so far:

\[(5x + 3)^2 + x^2 = 40000\] I then simplified and foiled and got;
\[25x^2+30x-39991=0\] Then I did the quadratic formula

Answer 3

(can't write it out completely in the equation tab)

x = -30 +/- sqrt 30^2 - 4(26)(39991) all over 2(26)

Answer 4

Here now I got it

\[x = \frac{ -30 \pm \sqrt{30^2 -4(26)(39991)}}{ 2(26) }\]