<s>[INST] Express the given polar equation in simplest rectangular form: $r = 4 + 3cosθ$ Express the given polar equation in simplest rectangular form: $r = 4 + 3cosθ$
My attempt
Multiplying r on both sides, we get
$r^2=4r+3 rcos\theta$
since, $x=rcos\theta$ and $y=rsin\theta$
and $r^2=x^2+y^2$
we get $x^2+y^2=4r+3x$
can anyone please explain after this step.. 
 [/INST] $$r^2 - 4 r = 3 x$$
$$x^2 +y^2 - 4\sqrt{x^2 +y^2} = 3 x$$
which represents a cardoid.. it is better to leave it that way.
if you try to get rid of radical sign you end up with another equation representing another symmetrical cardoid,  not  really what you wanted to represent at the outset: 
$$x^2 +y^2 + 4\sqrt{x^2 +y^2} = 3 x$$
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