How do i solve: 1/2(r+2)^2 = 1/3(2r-1)^2? The answer is supposed to be (-7+/-3√5)/2... how?

Question

anonymous · Answer

5r^2-14r-10=0 solve this one

anonymous · Answer

it's 1.02255386... if I use the quadratic formula.

anonymous · Answer

1,4+/-0,6*(11^0.5)

anonymous · Answer

what? I'm so confused..

turingtest · Answer

$$\frac12(r+2)^2=\frac13(2r-1)^2$$$$3(r+2)^2=2(2r-1)^2$$$$3(r^2+4r+4)=2(4r^2-4r+1)$$$$3r^2+12r+12=8r^2-8r+2$$$$5r^2-20r-10=0$$$$r^2-4r-2=0$$$$r=\frac{4\pm\sqrt{4^2-4(-2)}}{2}=2\pm\sqrt6$$...do I have the original problem right?

anonymous · Answer

yes you did. Why is it 3(r+2)^2 = 2(2r-1)^2?

anonymous · Answer

for the second step?

turingtest · Answer

multiply both sides by 6

anonymous · Answer

why by 6?

turingtest · Answer

to get rid of the fractions and make life easier

turingtest · Answer

(because 6 is the LCM of 2 and 3 if you want to think about it technically...)

anonymous · Answer

ohh, okay. I get it now, thank you!

turingtest · Answer

welcome, but it's not the answer you wanted...