Answer:
Step-by-step explanation:
The goal to solving any equation is to have x = {something}. That means we need to get the x out from underneath that radical. It's a square root, so we can "undo" it by squaring. Square both sides because this is an equation. Squaring both sides gives you
[tex]x^2=-3x+40[/tex]
Get everything on one side of the equals sign and set the quadratic equal to 0:
[tex]x^2+3x-40=0[/tex]
Throw this into the quadratic formula to get that the solutions are x = 5 and -8. We need to see if only one works, both work, or neither work in the original equation.
Does [tex]5=\sqrt{-3(5)+40}[/tex]?
[tex]5=\sqrt{-15+40}[/tex] and
[tex]5=\sqrt{25}[/tex]
and 5 = 5. So 5 works. Let's try -8 now:
[tex]-8=\sqrt{-3(-8)+40}[/tex] and
[tex]-8=\sqrt{24+40}[/tex] so
[tex]-8=\sqrt{64}[/tex]
-8 = 8? No it doesn't. So only 5 works. Your choice is the third one down.
